A NMOS Linear Voltage Regulator for
Automotive Applications
A THESIS
SUBMITTED TO THE FACULTY OF
ELECTRICAL ENGINEERING, MATHEMATICS
AND COMPUTER SCIENCE
OF DELFT UNIVERSITY OF TECHNOLOGY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF MASTER OF SCIENCE
Yang Li
October 2012
Members of the thesis defense committee:
Dr. ir. C.J.M. Verhoeven
Dr. ir. N.P. van der Meijs
Dr. ir. W.A. Serdijn
Ir. Th. Hamoen
©The work in this thesis was performed in NXP Semiconductors,
all rights are reserved.
i
Abstract
The electronization of automobiles is considered to be a revolution in automotive
technology development progress. One trend for automotive electronics design is pursuing higher level integration. System level integrated circuits are needed to simplify
the automotive electronics design and increase the reliability of automobiles.
In this thesis, a prototype of linear voltage regulator is designed for system level
integration. Instead of conventional PMOS linear regulator topology, a NMOS power
transistor is chosen as the pass device on considerations of smaller silicon area and
better dynamic performance. The characteristic differences of PMOS and NMOS
linear regulators are analyzed. Based on the frequency behavior analysis of these two
types of regulators, a frequency compensation scheme for the NMOS linear regulator
is purposed in this thesis. This purposed scheme is able to accommodate the wide
frequency variation of the NMOS linear regulator output pole. The effectiveness of
frequency compensation is examined by both mathematical modeling and transistor
level simulation. The over-current protection of the NMOS linear regulator is also
designed, which is realized by applying another current regulation loop to the voltage
regulator. This NMOS linear regulator is able to maintain a constant output current
around 250mA in over-current protection scenario.
Compared to the existing PMOS linear regulator counterpart, the off-chip ceramic
capacitor of this NMOS linear regulator can be reduced to 220nF (10x smaller) without sacrificing the ±2% output voltage accuracy within -40°C∼175°C. The regulator
quiescent current at no current load scenario is 12μA. Owing to the introduction of
adaptive biasing scheme, the maximum quiescent current is 1.31mA. This adaptive
biasing only degrades the current efficiency by maximum 4%.
At the end of the thesis, possible maximum load current and external capacitor
scaling abilities of this NMOS linear regulator are discussed.
ii
Acknowledgments
I am deeply grateful to all the people who helped me during this master thesis project.
Like every changeling project, the progress was made by countless failures. Without
the support of others, it would not be possible for me to reach this stage.
First and foremost, I would like to thank Dr. Chris Verhoeven and Ir. Thijmen
Hamoen for their guidance over this project. I really benefit a lot from their method
of doing electronic design. In addition, I am very grateful to them for the reviewing
of my thesis with great care and attention, and for their invaluable comments and
suggestions that contributed much to the improvement and completion of this thesis.
I would like to express my gratitude to my company supervisor Ir. Luc van Dijk.
As my daily supervisor, he gave me help not only during technical discussions, but
also in my daily life. I learned a lot from his way of working. Not many people before
have tried this NMOS linear regulator topic, it was not easy for us to find or invent
new solutions. I really appreciate his encouragement and patient during the hard
times of this project.
Special thanks go to colleagues in NXP Semiconductor, Nijmegen. I would like to
thank Gerald Kwakernaat for offering me this project. I am grateful to Dr. Klass-Jan
de Langen for many valuable discussions. I am truly lucky to have many experienced
colleagues: Harm Dekker, Nico Berckmans, Issa Niakate, etc. who gave me their
precious suggestions on this project.
I wish to thank Dr. Anton Bakker for both his lecture on power conversion technology and the discussion on the NMOS linear regulator design.
I would like to thank my friends at here. These go to Yang Liu and Jianghai He
for many collaborations on course projects; go to Yao Cheng, Xiaoliang Ge, Haoyan
Xue, Fengli Wang, Long Kong, Zhuowei Liu, etc. for happy times we spend in Delft;
go to Océane Gucher and Anthony Payét for the wonderful time together as student
interns in Nijmegen.
Words can not express my gratitude to my parents and family members for their
support and encouragement. Without their boundless love, I would never have had
the strength to chase my dreams, and for that I dedicated this thesis to them.
iii
Contents
1 Introduction
1.1 Power Management in Automotive Vehicles . . .
1.2 Linear Regulator and Switch Mode Power Supply
1.3 Pass Device in Liner Regulators . . . . . . . . . .
1.4 Motivations . . . . . . . . . . . . . . . . . . . . .
1.5 Organization of This Thesis . . . . . . . . . . . .
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2 Comparison of NMOS and PMOS Linear Regulators
2.1 Basic Topology . . . . . . . . . . . . . . . . . . . . . .
2.2 Static State Specifications . . . . . . . . . . . . . . . .
2.2.1 Drop-out Voltage . . . . . . . . . . . . . . . . .
2.2.2 Quiescent Current . . . . . . . . . . . . . . . .
2.2.3 Line Regulation . . . . . . . . . . . . . . . . . .
2.2.4 Load Regulation . . . . . . . . . . . . . . . . .
2.2.5 Temperature Drift . . . . . . . . . . . . . . . .
2.3 Dynamic State Specifications . . . . . . . . . . . . . .
2.3.1 Line Transient Response . . . . . . . . . . . . .
2.3.2 Load Transient Response . . . . . . . . . . . . .
2.4 High Frequency Specifications . . . . . . . . . . . . . .
2.4.1 Power Supply Rejection Ratio . . . . . . . . . .
2.4.2 Output Noise . . . . . . . . . . . . . . . . . . .
2.4.3 Electromagnetic Interference . . . . . . . . . . .
2.5 Frequency Behavior . . . . . . . . . . . . . . . . . . . .
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3 Design of NMOS Linear Voltage Regulator
3.1 Pass Device Characteristic and Sizing . . . . . . . . . . . .
3.2 NMOS Linear Regulator Topology . . . . . . . . . . . . . .
3.3 High Voltage Error Amplifier . . . . . . . . . . . . . . . .
3.4 Frequency Compensation . . . . . . . . . . . . . . . . . . .
3.4.1 Output Capacitor Sizing . . . . . . . . . . . . . . .
3.4.2 Small Signal Modeling . . . . . . . . . . . . . . . .
3.4.3 Proposed Compensation Scheme . . . . . . . . . . .
3.5 Adaptive Biasing . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Current Sensing for Adaptive Biasing . . . . . . . .
3.5.2 Frequency Compensation for Current Sensing Loop
iv
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3.5.3
3.5.4
3.5.5
3.6
Adaptive Biasing Current Ratio Consideration . . . . . . . . .
Adaptive Biasing Effect on Main Voltage Regulation Loop . .
Linear Regulator High Current Load Stability with Adaptive
Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Over-current Protection . . . . . . . . . . . . . . . . . . . . . . . . .
4 Performance Evaluations
4.1 Static Performance . . . . . . . . . . . . . . . . .
4.1.1 Drop-out Region . . . . . . . . . . . . . .
4.1.2 Quiescent Current and Current Efficiency
4.1.3 Static Output Voltage Accuracy . . . . . .
4.2 AC Performance . . . . . . . . . . . . . . . . . . .
4.3 Dynamic Performance . . . . . . . . . . . . . . .
4.3.1 Line Transient Response . . . . . . . . . .
4.3.2 Load Transient Response . . . . . . . . . .
4.4 High Frequency Performance . . . . . . . . . . . .
4.4.1 Power Supply Rejection . . . . . . . . . .
4.4.2 Output Noise . . . . . . . . . . . . . . . .
4.5 Over-current Protection Performance . . . . . . .
4.6 Overall Performance Summary . . . . . . . . . . .
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5 Scaling Features
5.1 External Capacitor Scaling . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Load Current Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
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6 Conclusions and Future Work
75
A Method for Simplifying the Transfer Function
76
B The Overall Transfer Function Calculation
78
C Matlab Codes
C.1 Gm Calculation . . . . . . . . . . . . . . . . .
C.2 Uncompensated Transfer Function Calculation
C.3 Transfer Function to the gate of MN . . . . .
C.4 Compensated Transfer Function Calculation .
C.5 Comparison of Bode Plot . . . . . . . . . . . .
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D Test-benches
85
E Current Sink Path
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v
List of Figures
1.1
1.2
1.3
2.1
A symplified automotive power management system. .
A typical ECU diagram. . . . . . . . . . . . . . . . . .
DC voltage converter topology (a) linear regulator and
regulator. . . . . . . . . . . . . . . . . . . . . . . . . .
. .
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(b)
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switching
. . . . . .
2
2
3
2.9
2.10
2.11
2.12
2.13
Basic linear regulator topology with (a) PMOS as pass device (b)
NMOS as pass device. . . . . . . . . . . . . . . . . . . . . . . . . . .
Lead-acid discharge curves under a constant load current. . . . . . . .
Transient response of (a) PMOS regulator (b) NMOS regulator. . . .
One possible PMOS linear regulator line transient response (a) with
infinite bandwidth (b) with finite bandwidth. . . . . . . . . . . . . . .
One possible NMOS linear regulator line transient response (a) with
infinite bandwidth (b) with finite bandwidth. . . . . . . . . . . . . . .
One possible PMOS linear regulator load transient response (a) with
infinite bandwidth (b) with finite bandwidth. . . . . . . . . . . . . . .
One possible NMOS linear regulator load transient response (a) with
infinite bandwidth (b) with finite bandwidth. . . . . . . . . . . . . . .
(a) Power supply rejection on linear regulator (b) typical bode plot of
PSRR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equivalent input noise of linear regulator. . . . . . . . . . . . . . . .
EMI example in automotive environment. . . . . . . . . . . . . . . .
A simple topology of (a) PMOS regulator (b) NMOS regulator. . . .
Bode plot of (a) PMOS regulator (b) NMOS regulator. . . . . . . . .
P2 movement over load current. . . . . . . . . . . . . . . . . . . . . .
17
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20
20
22
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
Power MOS symbol and the cross section view. . . . . . . . . . . . .
NMOS linear regulator topology. . . . . . . . . . . . . . . . . . . . .
High voltage operational amplifier with cascode low voltage input pair.
Small signal equivalent of NMOS linear regulator. . . . . . . . . . . .
Transconductance of NMOS power transistor. . . . . . . . . . . . . .
Transfer function calculation. . . . . . . . . . . . . . . . . . . . . . .
Compensation scheme of Method (2). . . . . . . . . . . . . . . . . . .
Adding a zero and its associated pole. . . . . . . . . . . . . . . . . . .
Adding a zero while merging the associated pole with dominate pole.
Integrator configuration with C2 . . . . . . . . . . . . . . . . . . . . .
Bode plot at IL =0μA. . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.2
2.3
2.4
2.5
2.6
2.7
2.8
vi
6
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16
3.22
3.23
3.24
3.25
3.26
3.27
3.28
3.29
3.30
3.31
3.32
Simplified bode plot analysis at IL =0μA. . . . . . . . . . . . . . . . .
Phase margin analysis at IL =0μA. . . . . . . . . . . . . . . . . . . .
Bode plot at full load current IL =120mA. . . . . . . . . . . . . . . .
Stability analysis at high load current. . . . . . . . . . . . . . . . . .
Illustration of adaptive biasing idea. . . . . . . . . . . . . . . . . . . .
Current sensing scheme with regulated source node voltage. . . . . .
Small signal equivalent of current sensing loop. . . . . . . . . . . . . .
Current sensing loop bode plot at IL = 0μA. . . . . . . . . . . . . . .
Current sensing loop bode plot at IL =120mA. . . . . . . . . . . . . .
Phase margin and bandwidth versus load current for current sensing
loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Adaptive biasing on the main voltage feedback loop stability analysis.
Adaptive biasing current versus load current IL . . . . . . . . . . . . .
Adaptive biasing loop gain plot. . . . . . . . . . . . . . . . . . . . . .
Linear regulator high current load bode plot with adaptive biasing . .
Current limitation scheme. . . . . . . . . . . . . . . . . . . . . . . . .
Over-current limitation. . . . . . . . . . . . . . . . . . . . . . . . . .
Over-current limitation schematic. . . . . . . . . . . . . . . . . . . . .
Current limitation simplified loop for stability analysis. . . . . . . . .
Current limitation loop bode plot (RL =10Ω). . . . . . . . . . . . . .
Current limitation stability over RL . . . . . . . . . . . . . . . . . . .
Main voltage regulation loop gain plot over RL . . . . . . . . . . . . .
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56
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
VOU T versus VBAT (VCP =10V, typical process corner, temp=27°C). .
Iq versus IL (VBAT =12V, typical process corner, temp=27°C). . . . .
Current efficiency (VBAT =12V, typical process corner, temp=27°C). .
Static line regulation (IL =120mA, typical process corner). . . . . . .
Static load regulation(VBAT =12V, typical process corner). . . . . . .
Ouput voltage spread (VBAT =12V,IL =0,-40°C∼175°C). . . . . . . . .
Bode plot over different IL . . . . . . . . . . . . . . . . . . . . . . . . .
Phase and gain margin versus IL . . . . . . . . . . . . . . . . . . . .
Bandwidth versus IL . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Low battery line transient response (IL =120mA, -40°C∼175°C). . . .
High battery line transient response(IL =120mA, -40°C∼175°C). . . .
Load transient response (VBAT =12V,-40°C∼175°C). . . . . . . . . . .
Low current load transient response (VBAT =12V,-40°C∼175°C). . . .
Staircase load transient response (VBAT =12V,-40°C∼175°C). . . . . .
PSRR over IL (VBAT =12V,typical process corner, 27°C). . . . . . . .
Output noise (IL =20mA,typical process corner, 27°C). . . . . . . . .
IL versus RL (VBAT =12V, typical process corner). . . . . . . . . . . .
Over-current protection transient behavior (VBAT =12V,-40°C∼175°C).
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69
5.1
5.2
5.3
Phase margin among output capacitor sizing range. . . . . . . . . . .
Bandwidth at high current load over CL . . . . . . . . . . . . . . . . .
Load transient response (IL increasing) with different CL . . . . . . . .
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71
72
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
vii
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40
41
42
43
44
44
46
47
Load transient response (IL decreasing) with different CL . . . . . . .
A 1A linear regulator load transient response. . . . . . . . . . . . . .
72
74
B.1 Signal signal model for the whole loop. . . . . . . . . . . . . . . . . .
78
D.1 Test-benches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2 RT EST waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
85
E.1 Without current sink path. . . . . . . . . . . . . . . . . . . . . . . . .
E.2 Current sink path circuit. . . . . . . . . . . . . . . . . . . . . . . . .
E.3 With current sink path. . . . . . . . . . . . . . . . . . . . . . . . . .
86
87
88
5.4
5.5
viii
List of Tables
1.1
1.2
Comparison of Linear and Switching Regulators . . . . . . . . . . . .
Performance Characteristics of the PMOS Linear Regulator . . . . .
4
5
3.1
3.2
Components Parameters of the NMOS Linear Regulator . . . . . . .
Poles and Zeros Location of the Whole Loop . . . . . . . . . . . . . .
31
38
4.1
Overall NMOS Linear Regulator Performance Summary . . . . . . . .
69
5.1
Load Current Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
ix
Chapter 1
Introduction
Ever since the first modern automotive vehicle was built in Mannheim, Germany by
Karl Benz in 1885 [1], it has changed the human society in a great deal. The invention of automotive vehicles shortened the distance between individuals and brought
more convenience to human beings. The automobile is always considered as one of the
greatest inventions of the 20th century. With the increasing development of electronic
technology since 1950s, electronic devices embedded in automobile has shown significant advantages in aspects of controllability, comfortability and safety. Electronic
components currently comprise 20-30% of total costs for all automotive categories,
this figure is expected to reach 40% or so by 2015 [2]. In this thesis we will discuss
power management in automotive vehicle and focus on NMOS linear voltage regulator
design.
1.1
Power Management in Automotive Vehicles
Beside the huge mechanical system, a modern automobile vehicle can also be recognized as a complex electrical system. Power management is an indispensable part
of the electrical system, which provides separate supply voltage and current driving
capabilities. Take the Audi A8 for an example, the electric front screen heating is
with an approximate power consumption of 1000 Watts1 , the car audio system is
powered by 12V and consumes 80 Watts on average2 . With more and more electrical
modules installed on cars, both the increasing power consumption and load versatility
complicate the power management system.
Figure 1.1 shows a simplified power management system in a car. This system
handles the battery charging through a generator (stator and rectifier). The generator
voltage control is used to regulate the generator output voltage to 12V. The battery
is supplying power to separate electronic control units (ECUs) and other electric
modules.
ECU is an embedded system that controls one or more electrical systems or subsystems. Modern automotive vehicles can feature up to 70 ECUs, such as airbag
1
2
Source: Bosch and ADL research
Source: Wikipidia and ADL research
1
CHAPTER 1. INTRODUCTION
Generator
Voltage
Control
ECU1
Rectifier
ECU2
12V
Battery
Stator
Others
Figure 1.1: A symplified automotive power management system.
control unit, body control module3 , engine control unit, brake control module and so
on.
An example of an automotive ECU is shown in Figure 1.2. It consists of power
management, data transmitting and receiving, micro-controlling, sensing and actuation modules. The ECU is powered by a typical value 12V lead-acid battery. Normally, many electronic devices inside the ECU need lower voltage than this battery
supply. Therefore, a power management module with DC voltage conversion is essential. To communicate with other modules, transmitters and receivers are included
in the “In Vehicle Networking” part. Micro-controller is the central processing unit
of the ECU. Sensors and actuators are modules which can acquire and transfer data
between electronic domain and other domains.
VBAT
Power
Supply
Sensors
Microcontroller
Data
In Vehicle
Networking
Actuators
Figure 1.2: A typical ECU diagram.
3
Which controls door locks, electric windows, etc.
2
CHAPTER 1. INTRODUCTION
1.2
Linear Regulator and Switch Mode Power Supply
A linear voltage regulator is a DC voltage converter which realizes its function by
linearly regulating the input DC voltage to a lower output DC voltage, as shown
in Figure 1.3(a). Since the output voltage is linearly regulated, it has advantages
in aspects of dynamic response, output noise and power supply rejection, etc. The
major disadvantage of linear regulator is the power conversion efficiency. When the
load current is high, the power loss can be dramatic. This makes linear regulator not
a suitable candidate for some systems where large output currents are required.
VIN
VIN
VREF
VREF
Pass
Device
Amp
Amp
Digital
Pulse
Modultion
VOUT
Feedback
RL
VOUT
CL
RL
Feedback
(a)
(b)
Figure 1.3: DC voltage converter topology (a) linear regulator and (b) switching
regulator.
Switch mode power supply (SMPS) is a type of switching regulator which realizes
power conversion with a control mechanism in the discrete time domain, as shown in
Figure 1.3(b). Generally, at least one energy store component (either an inductor or
a capacitor) is required in a SMPS. The fundamental principle of SMPS and linear
regulator is similar. For a switching regulator, there is also a feedback loop that
regulates the output voltage to its desired value. If the output voltage is not as
expected, the discrete time control will decide to charge or discharge the energy store
component by modulating the pulse width or frequency. The advantage of switching
regulator is its efficiency can easily reach up to 80%∼90% or even higher [3]. The
drawbacks are in aspects of dynamic response, output ripple and cost. The dynamic
response of switching regulator can be affected by its limited bandwidth. The output
ripple is caused by switching activities. The higher cost of switching regulator comes
from design complexity and off-chip components. For an inductor based switching
regulator, the off-chip component may include an inductor and a capacitor, while
the linear regulators may only have one external capacitor, which is cheaper. The
comparison of linear and switching regulator is shown in Table 1.1.
3
CL
CHAPTER 1. INTRODUCTION
Table 1.1: Comparison of Linear and Switching Regulators
Linear regulator
Switching regulator
Output range
VOUT <VIN
VOUT <VIN or VOUT >VIN
Dynamic response
Fast
Slow
Efficiency
Low
High
Noise
Low
High
Cost
Low
High
1.3
Pass Device in Liner Regulators
The pass device in a linear regulator is generally a transistor with a large size. This
transistor must be able to handle the maximum load current without causing over
temperature and reliability issues. To realize a low drop-out voltage at high current load, the conducting resistance of the pass transistor in linear region should be
extremely low. Therefore, a very large transistor size is needed.
The pass transistor can either be a BJT or a MOSFET. Classical linear regulators
such as LM78xx are using BJT based pass transistors. In state-of-the-art designs,
MOSFETs are widely used because on-chip system integration (e.g. a mixed-signal
system) can benefit from CMOS technology.
The pass device can be a n-type or p-type transistor. Generally, for the same
size, the n-type transistor has a higher current conduction ability than the p-type
one4 . However, in order to easily achieve a low drop-out voltage regulation (as will be
discussed in Section 1.4), p-type transistors are preferred in many regulator designs
although they are with a lower current conduction ability.
1.4
Motivations
PMOS as the pass device is the most popular choice, owing to its gate voltage always
lower than the supply rail. For NMOS as the pass device, the gate voltage is higher
than supply if operating in low drop-out region. Therefore, an additional circuit such
as a charge pump should be added which brings more design complexity. However,
NMOS as the pass device has its advantages. First, it consumes smaller silicon area
for the same maximum output current specification. Second, for a NMOS linear
regulator, the transistor source node is directly connected to the regulator output
node, which is actually a source follower with “local feedback” characteristic. This
might provide a better dynamic performance in large signal domain.
The aim of this thesis is to investigate if NMOS linear regulator is able to achieve a
comparable performance with its PMOS equivalent one (the equivalent PMOS linear
regulator design is already available). Moreover, since the NMOS output stage may
have a better dynamic performance, there might be a chance to reduce the load
capacitance (2.2μF in the available PMOS linear regulator design).
4
The hole movement involves in breaking and forming covalent bonding, while electrons are much
freer to move, therefore electrons has a higher mobility
4
CHAPTER 1. INTRODUCTION
The drawback of NMOS linear regulator is also prominent. In low drop-out region,
voltage boost techniques may introduce switched capacitor circuits. It will reduce the
NMOS linear regulator area efficiency, generate ripples at the output and increase the
power consumption.
The performance characteristics of the available PMOS linear regulator is summarized in Table 1.2. The NMOS linear regulator should be designed within these
specifications while trying to minimize the silicon area and external output capacitance.
Table 1.2: Performance Characteristics of the PMOS Linear Regulator
Symbol
Parameter
Min Typ Max
VIN
Regulator Input Voltage
5.5
40
VOUT
Output Voltage
4.9
5.0
5.1
ΔVout load
Dynamic Load Regulation
-2
+2
tstabilized output voltage within 0.5% after load step
1
ΔVout line
Dynamic Line Regulation
-2
+2
Iq
Quiescent Current(w/o band-gap)
10
CL
External Output Capacitor
2.2
-
1.5
Unit
V
V
%
ms
%
μA
μF
Organization of This Thesis
This thesis consists of six chapters. In Chapter 2, the PMOS and NMOS linear regulators are compared. The aim is to briefly introduce the linear regulator specifications
with analysis of PMOS and NMOS as pass device respectively. This will build the
foundation of the regulator design in this thesis.
In Chapter 3, the design of NMOS linear regulator is presented. First, small
signal behavior of the main voltage feedback loop is accurately analyzed and modeled.
Then, a compensation scheme which is able to add a zero without being troubled by its
associated pole is proposed. After that, an adaptive biasing scheme is implemented to
further increase the bandwidth of the main regulation loop. Finally, the over-current
protection circuit design is discussed.
In Chapter 4, the performance evaluations based on detailed simulations of the
designed NMOS linear regulator are presented.
Chapter 5 introduces scaling features of the designed NMOS regulator. In the first
part, the external capacitor range of this linear regulator is discussed. The second
part focuses on design recommendations for this linear regulator to adapt for different
maximum load current specifications.
Finally, Chapter 6 presents conclusions of this thesis and gives suggestions for
future works.
5
Chapter 2
Comparison of NMOS and PMOS
Linear Regulators
In this Chapter, specifications of linear regulator will be discussed based on the comparison of PMOS and NMOS as the pass device. In the end, the AC characteristic of
these two linear regulator topologies will be analyzed.
2.1
Basic Topology
Figure 2.1 shows the basic linear regulator topologies with PMOS and NMOS as the
pass device respectively. The analysis of linear regulator specifications is based on
this figure.
VIN
VIN
VREF
VREF
Av
MP
Av
MN
VOUT
VOUT
R1
Vfb
Iload
RL
R1
Vfb
CL
Iload
RL
CL
R2
R2
(a)
(b)
Figure 2.1: Basic linear regulator topology with (a) PMOS as pass device (b) NMOS
as pass device.
6
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
2.2
2.2.1
Static State Specifications
Drop-out Voltage
The drop-out voltage is defined as the minimum voltage difference between VIN and
VOU T (Figure 2.1) to maintain an intended voltage regulation [4]. A linear regulator
which can operate in low drop-out voltage regulation is commonly named as low
drop-out regulator (LDO). There is no universal agreement on how much drop-out
voltage makes one voltage regulator a “LDO”. Literature [5] defines a regulator with
a drop-out voltage below 600mV in battery-operated environments is a LDO. In stateof-the-art design, the drop-out voltages are normally in the range of 200∼500mV.
2.2.2
Quiescent Current
The quiescent current1 (Iq ) is defined as the current consumed by the linear regulator
control circuits. The power efficiency η of a linear regulator can be expressed in
Equation 2.1, where Iload is current flowing into the load, Vdrop−out is the drop-out
voltage.
η=
VOU T Iload
Iload
Edeliverd
Vdrop−out
= (1 −
=
)
Esupplied
VIN (Iload + Iq )
VIN
Iload + Iq
(2.1)
Both reducing Vdrop−out and Iq will increase the efficiency. The linear regulator efficiency is changing over Iload variation. As Iload is much larger than Iq , the
Iload /(Iload + Iq ) term2 approximately equals to 1, the dominate factor affecting power
efficiency is Vdrop−out .
2.2.3
Line Regulation
Line regulation represents the ability of a regulator to withstand static variations
from its supply. It is defined as a gain between regulated output and input supply
ΔVOU T /ΔVIN . The static supply voltage variation might be caused by the battery
voltage reduction during one discharge cycle. Figure 2.2 shows an estimated lead-acid
battery discharge curve and its regulated output.
Ideally, the regulated voltage should be fixed until the regulation losing its effectiveness. However, due to the finite loop gain, the output voltage actually varies with
supply voltage. It should be noted that even line regulation is a DC specification, it
would be easier to analyze it in small signal domain. The analysis starts from the
PMOS regulator shown in Figure 2.1(a), suppose the transconductance of MP is gmp ,
its output resistance is ro,p , Av is the open-loop gain of the amplifier. Now assume
a small variation happens at the VIN node by ΔVIN , the VOU T node should have a
correspondent voltage variation by ΔVOU T . The equation can be set up as:
1
2
Also named as ground current Ignd
Which is the current efficiency
7
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
Voltage
12V
Battery(i.e. Lead-acid)
Regulated Voltage
5V
Time
Figure 2.2: Lead-acid discharge curves under a constant load current.
R2
Av )gmp [(R1 + R2 )||RL ||ro,p ] = ΔVOU T
(2.2)
R1 + R2
Normally, the term gmp [(R1 + R2 )||RL ||ro,p ] can be much greater than 1 in most
cases, Equation 2.2 can be simplified as:
(ΔVIN − ΔVOU T
ΔVOU T
=
ΔVIN
gmp [(R1 + R2 )||RL ||ro,p ]
1
≈
(2.3)
R2
R2
1 + gmp [(R1 + R2 )||RL ||ro,p ]Av
Av
R1 + R2
R1 + R2
From Equation 2.3, it shows that increasing Av will improve the line regulation.
The line regulation analysis of NMOS regulator is based on Figure 2.1(b). Again,
the transconductance of MN is gmn , the output resistance is ro,n , Av is the open loop
gain of the amplifier. The Equation of ΔVIN variation on ΔVOU T is:
R2
ΔVIN − ΔVOU T
Av − ΔVOU T )gmn +
][(R1 + R2 )||RL ] = ΔVOU T
R1 + R2
ro,n
(2.4)
The line regulation of the NMOS regulator can be expressed as:
[(−ΔVOU T
ΔVOU T
=
ΔVIN
1
R2
ro,n
(1 +
Av )gmn ro,n +
+1
R1 + R2
(R1 + R2 )||RL
(2.5)
ro,n
is a number which is much
It is interesting to notice that the term (R1 +R
2 )||RL
R2
smaller than (1 + R1 +R2 Av )gmn ro,n . It can be proved as follows:
1
1
ro,n
λI
= load =
V
(R1 + R2 )||RL
λVOU T
OU T
Iload
8
(2.6)
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
For common analog process (e.g. 0.5μm gate length), the channel length modulation factor λ is around 0.1 [6]. Therefore, according to Equation 2.6, the term
ro,n
2
is much smaller than (1 + R1R+R
Av )gmn ro,n , for the latter one is almost a
(R1 +R2 )||RL
2
multiplication of Av and intrinsic NMOS transistor gain gmn ro,n .
Then, Equation 2.5 can be simplified as:
ΔVOU T
≈
ΔVIN
1
R2
Av gmn ro,n
R1 + R2
(2.7)
From Equation 2.7, the line regulation for NMOS regulator is related to Av and
the NMOS transistor intrinsic gain gmn ro,n . Compared with PMOS regulator line
regulation result (Equation 2.3), the NMOS regulator has an improved line regulation
by gmn ro,n . This result makes sense because the NMOS pass device is acting as a
“cascode” transistor between VIN and VOU T . If a variation adds on the drain node of
a regulated NMOS transistor, its equivalent variation on the source node should be
attenuated by the transistor intrinsic gain and the amplifier open-loop gain Av .
2.2.4
Load Regulation
The load regulation is defined as the static output voltage variation (ΔVOU T ) in
response to static load current changes (ΔIOU T ). The PMOS load regulation analysis
is based on Figure 2.1(a). Again, the small signal analysis is used, Av is the amplifier
open-loop gain, gmp is the transconductance of PMOS, Iload is the current load flow
through RL (assume R1 and R2 are much larger than RL ). The relation between the
output voltage variation and load current is:
− ΔVOU T
R2
Av gmp = ΔIload
R1 + R2
(2.8)
Therefore, the ΔVOU T /ΔIload is:
ΔVOU T
=−
ΔIload
1
R2
Av gmp
R1 + R2
(2.9)
From Equation 2.9, the load regulation ability is determined by Av and gmp .
The NMOS regulator load regulation analysis is based on Figure 2.1(b). Again,
Av is the amplifier open-loop gain, gmn is the NMOS transconductance, Iload is the
current load flow through RL . The transfer function of load current variation on
output voltage is:
(−ΔVOU T
R2
Av − ΔVOU T )gmn = ΔIload
R 1 + R2
The expression of ΔVOU T /ΔIload is:
9
(2.10)
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
ΔVOU T
=−
ΔIload
1
1
≈−
(2.11)
R2
R2
(
Av + 1)gmn
Av gmn
R1 + R2
R 1 + R2
It is found that for the NMOS regulator, the load regulation is also dependent on
Av and gmn .
2.2.5
Temperature Drift
The temperature variation also affects the linear regulator output voltage accuracy.
Linear regulator temperature coefficient (TC) is defined as the percentage of output
voltage variation in response to temperature change [5], which has a unit of %/ . It
can be expressed as:
‰
TC =
1
VOU T
ΔVOU T
=
ΔT
(ΔVREF + ΔVOS )(
VOU T ΔT
VOU T
)
VREF
=
ΔVREF + ΔVOS
VREF ΔT
(2.12)
ΔT represents the temperature changes, ΔVREF and ΔVOS are reference voltage
and input equivalent offset variation according to temperate change. From Equation 2.12, the temperature impaction on output voltage is directly dependent on the
temperate coefficient of reference voltage (ΔVREF /ΔT ) and the temperate coefficient
of input equivalent offset voltage (ΔVOS /ΔT ).
2.3
Dynamic State Specifications
The abilities of linear regulator in response to supply voltage and load current transient variation are two major dynamic state specifications. The output voltage spike
and recovery time affect the regulator output accuracy, which degenerates the quality of output voltage. Good transient response with small output voltage variation
including overshoots and undershoots is critical to prevent an accidental turn off or
resetting of the load device [7]. The output voltage spike is in large signal domain,
where slewing and non-linear behavior happen. Therefore, it is difficult to accurately
define the spike voltage and recovery time.
In this section, the transient behavior is divided into a few time periods. It
is possible to qualitatively analyze the transient behavior at each time period. A
comparison of linear regulators with infinite and finite bandwidth is analyzed based
on Figure 2.3.
10
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
line
VIN,max
transient
VIN
VIN,min
variation
IMOS
VREF
Ramp
Av
VG
Camp
MP
R1
Vfb
IMOS
Ramp
Av
VOUT
VG
Camp
ICAP
CL
R2
VIN
VREF
IL,max
IL,min
IL
load
transient
variation
(a)
line
VIN,max
transient
VIN,min
variation
MN
R1
Vfb
VOUT
ICAP
CL
R2
IL,max
IL,min
IL
load
transient
variation
(b)
Figure 2.3: Transient response of (a) PMOS regulator (b) NMOS regulator.
2.3.1
Line Transient Response
Line transient response is the output voltage transient variation (VOU T in Figure 2.3)
in response to the supply voltage (VIN ) suddenly changes. In automotive environment, the supply voltage variation can be caused by car cranking3 , electromagnetic
inferences, noise, etc.
In this subsection, the line transient response of PMOS and NMOS regulator will
be discussed separately. A possible line transient response of PMOS regulator is
shown in Figure 2.4, where (a) is a feedback loop with infinite bandwidth, (b) is with
finite bandwidth. In (a), as the supply voltage VIN suddenly jumps up and down,
the gate voltage VG immediately follows the VIN , which makes VOU T , IM OS , ICAP
unchanged.
In (b), limited bandwidth will make VOU T vary with VIN . The transient behavior
can be divided into the following t1 − t9 time periods:
At t1 , the VIN and VG are kept at their nominal value. It should be noted that at
this time IM OS is at medium current load, which makes the regulator able to adjust
output current up and down4 .
At t2 , VIN suddenly goes up. Due to the limited bandwidth, VG begins to slew,
VSG is larger than t1 . The increased IM OS current flows into the load capacitor CL ,
which leads to an increased VOU T .
At t3 , the slew period ends. Both IM OS and ICAP excursions (compare to their
nominal value at t1 ) are reducing. The regulation loop begins to take control of VOU T .
At t4 , the regulation loop controls VOU T back to its nominal value. The curve is
sort of RC discharging, the time constant is related to the loop bandwidth.
At t5 , VG reaches its maximum. The VSG is the same with t1 .
3
Cranking is referred to as the voltage drop of the car battery during engine starting
If IM OS is in its minimum, VOU T can be at a voltage higher than nominal for a while since the
regulator has only source ability and no sink capability to its load
4
11
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
t1
t2
t3
t5 t6 t7 t8
t1 t2 t3 t4
t9
Voltage
Voltage
VSG
VSG
VIN
VSG
VIN
VSG
VG
VG
Time
Time
VOUT
VOUT
Time
Time
IMOS
IMOS
Time
Time
ICAP
ICAP
0
0
Time
t1
t2
Time
t5
t1 t2 t3 t4
t3
t6 t7 t8
t9
(b)
(a)
Figure 2.4: One possible PMOS linear regulator line transient response (a) with
infinite bandwidth (b) with finite bandwidth.
At t6 , VIN suddenly rolls down. Again, VG starts to slew. IM OS suddenly reduces,
ICAP is providing current to compensate the current difference (IM OS +ICAP =IL , assume IL is constant during line transient).
At t7 , the slew period ends, VOU T is gradually controlled by the feedback loop.
Both IM OS and ICAP excursions (compare to their nominal value at t1 ) are reducing.
At the end of t7 , VOU T reaches its minimum value.
At t8 , the feedback loop fully takes over the control of VOU T . VOU T is back to its
nominal value like a RC curve. The time constant of the RC curve is related to the
loop bandwidth.
12
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
At t9 , the line transient is over, the status is the same with t1 .
The line transient response of NMOS linear regulator is shown in Figure 2.5,
where (a) is with infinite bandwidth, (b) is with finite bandwidth. For the infinite
bandwidth case, no matter how the supply voltage VIN varies, the VOU T is kept at its
nominal value. The finite bandwidth transient behavior is divided into t1 − t9 time
periods. Each period will be discussed as follows:
t1
VIN
t2
t3
t1 t2 t3 t4
VIN
t5 t6 t7 t8
t9
VIN
VIN
Time
Voltage
Time
Voltage
VG
VG
VGS
VGS
VGS
VOUT
VOUT
Time
Time
IMOS
IMOS
Time
Time
ICAP
ICAP
0
0
Time
t1
t2
Time
t1 t2 t3 t4
t3
(a)
t5 t6 t7 t8
t9
(b)
Figure 2.5: One possible NMOS linear regulator line transient response (a) with
infinite bandwidth (b) with finite bandwidth.
At t1 , VIN and VOU T are at their nominal value. Again, IM OS is assumed to be
providing medium current load.
At t2 , VIN suddenly goes up. Due to channel length modulation, IM OS starts to
provide additional current. This current is directly charged into CL (assume IL is
constant), which makes VOU T suddenly increase. VG starts to slew to follow the fast
VOU T variation.
13
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
At t3 , VG is controlled by the feedback loop. IM OS and ICAP excursions (compare
to their nominal value at t1 ) reduce. At the end of t3 , the VGS is adjusted to its
nominal value (the same with t1 ), and VOU T is at its maximum value.
At t4 , the regulation loop fully takes over and regulates VOU T back to its nominal
value.
At t5 , all the voltages are at their nominal value.
At t6 , VIN suddenly rolls down. Again, IM OS is reducing owing to channel length
modulation, VOU T immediately decreases. The current difference between IL and
IM OS is compensated by ICAP . The fast VOU T rolling down causes VG starting to
slew.
At t7 , VGS is near its nominal value. IM OS and ICAP excursions (compare to their
nominal value at t1 ) is decreasing. By the end of t7 , the VOU T is at its minimum.
At t8 , the feedback loop fully takes over and regulates VOU T back to its nominal
value.
At t9 , the line transient is over, the status is the same with t1 .
2.3.2
Load Transient Response
Load transient response is defined as the linear regulator’s ability to regulate the
output voltage during fast load transients [8]. In practical cases, the circuit loaded by
a linear regulator can be dynamic (e.g. a micro-controller operating at several tens
of MHz), the load current variation is fast and unpredictable. The output voltage
changes in response to maximum load current variation at given period of time should
be defined for a linear regulator. In this subsection, the load transient behavior will
be analyzed in detail.
One possible load transient waveform of a PMOS linear regulator is shown in
Figure 2.6, where (a) is with infinite bandwidth. During load transient variation,
IL is provided by the power transistor current IM OS . The output voltage VOU T is
unchanged. (b) is with finite bandwidth, its transient behavior is divided into a few
time periods, the analysis is as follows:
At t1 , IL and VSG are at their nominal value.
At t2 , IL rises up immediately. Due to the loop delay, the major current for IL
variation is provided by ICAP . Charge flowing out of CL causes VOU T decease. Since
IL rising edge can be very fast (e.g. 60mA/μS), the fast variation which beyond the
loop bandwidth makes VG slewing.
At t3 , IM OS becomes the dominate source providing the load current IL . The
feedback loop gradually controls VOU T (slew period ends). For ICAP is reducing, the
speed of VOU T rolling down is reduced in comparison with time period t2 .
At the beginning of t4 , IM OS =IL , ICAP = 0. VOU T reaches its minimum value.
Then the loop begins to regulate VOU T back to its nominal value. The discharge curve
can be roughly modeled as a RC curve.
At t5 , VOU T is back to its nominal value, VSG is at its maximum which provides
the maximum load current IL,max .
At the beginning of t6 , IL goes down from IL,max to IL,min . Again, this current
variation is mainly provided by ICAP . The fast VOU T variation causes slewing on VG .
14
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
t1
t2
t3
t5 t6 t7 t8
t1 t2 t3 t4
Voltage
t9
Voltage
VIN
VSG,min
VIN
VSG,min
VSG,min
VSG,max
VG
VSG,min
VSG,max
VG
Time
Time
VOUT
VOUT
Time
Time
IMOS
IMOS
IL,max
IL,max
IL,min
IL,min
IL,min
IL,min
Time
Time
ICAP
ICAP
0
IL,max
0
-IL,max
Time
Time
IL
IL
IL,max
IL,max
IL,min
t1
IL,min
t2
(a)
IL,min
Time
IL,min
t5 t6 t7 t8
t1 t2 t3 t4
(b)
t3
Time
t9
Figure 2.6: One possible PMOS linear regulator load transient response (a) with
infinite bandwidth (b) with finite bandwidth.
At t7 , ICAP excursions is decreasing. The feedback loop takes the control of VOU T .
Finally, ICAP =0, and VOU T reaches its maximum.
At t8 , the loop fully takes over the control and VG is increasing as a RC curve.
At t9 , the load transient is over, the status is the same with t1 .
15
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
One possible NMOS linear regulator load transient response is shown in Figure 2.7,
where (a) is with infinite bandwidth. As the load current suddenly varies from IL,min
to IL,max , the gate voltage VG is fast enough to directly rise up to the expected
VGS,max . In the whole process, the output voltage VOU T is unchanged. (b) is with
finite bandwidth, the waveform is analyzed based on the divided a few time periods.
Voltage
t1
t2
t3
Voltage
t5 t6 t7 t8
t1 t2 t3 t4
t9
VG
VGS,min
VG
VGS,max
VGS,min
VGS,min
VGS,max
VGS,min
VOUT
VOUT
Time
Time
IMOS
IMOS
IL,max
IL,max
IL,min
IL,min
IL,min
IL,min
Time
Time
ICAP
ICAP
0
0
IL,max
-IL,max
Time
Time
IL
IL
IL,max
IL,max
IL,min
t1
IL,min
t2
(a)
IL,min
Time
t5 t6 t7 t8
t1 t2 t3 t4
(b)
t3
IL,min
Time
t9
Figure 2.7: One possible NMOS linear regulator load transient response (a) with
infinite bandwidth (b) with finite bandwidth.
At t1 , IL and VOU T are at their nominal value.
At the beginning of t2 , IL suddenly increases to IL,max . The majority of current
IL is provided by ICAP . Charges flowing out of CL will make VOU T roll down at very
fast speed. The decreasing VOU T will feedback to the input of the amplifier. If the
VOU T variation speed is beyond bandwidth, it will cause VG slewing.
16
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
At t3 , VGS is becoming larger and IM OS is the dominate source providing IL,max .
For ICAP excursion is reduced, the VOU T rolling down speed is slower than t2 period.
At the end of period t3 , the IM OS equals to IL,max , VGS reaches VGS,max , ICAP =0.
VOU T is at its minimum value.
At t4 , the feedback loop takes over the control of VOU T . The VOU T rising curve
can be treated as RC charging.
At t5 , VOU T is at the nominal value, IM OS and VGS are at their maximum.
At t6 , the load current is rolling down from IL,max to IL,min . At the very beginning
of t6 , due to bandwidth limitation VGS is still around VGS,max . The current difference
between IM OS and IL will be provided by ICAP , which is a current flowing into the
capacitor. VOU T is rising up at a very fast speed, which makes VG slewing down.
At t7 , IM OS is reducing, the loop gradually takes over the control of VOU T . The
amount of ICAP is decreasing as the difference between IM OS and IL are becoming
smaller and smaller. VOU T is increasing at a slower speed in comparison with t6
period.
At the beginning of t8 , IM OS =IL , ICAP =0, VOU T is at its peak value. The regulation loop fully takes over the control of VOU T . VOU T goes back to its nominal value
by a RC discharging curve.
At t9 , the load transient is over, the status is the same with t1 .
2.4
High Frequency Specifications
2.4.1
Power Supply Rejection Ratio
The power supply rejection of a linear regulator can be defined as the ability to
maintain a constant voltage VOU T in the presence of noisy VIN [9]. Figure 2.8(a)
shows a linear regulator attenuating the supply noise appearing at the regulated
output.
Noisy Supply Line
Linear
Regularor
PSRR(dB)
VIN
VOUT
Line
Regulation
(DC)
Loading
Blocks
PSRR
(AC)
GND
Freq(Hz)
Figure 2.8: (a) Power supply rejection on linear regulator (b) typical bode plot of
PSRR.
In comparison with the line regulation ability as discussed in Section 2.2, power
17
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
supply rejection ratio (PSRR) is in AC domain. Therefore, the small signal analysis
should be used. The PSRR is defined as:
P SRR = |20log10 (
VOU T
)|
VIN
(2.13)
A typical bode plot of PSRR is shown in Figure 2.8(b). In low frequency range,
the supply variation can be treated as a DC component, which is actually the line
regulation discussed in Section 2.2.3. As frequency increases, more noise or ripple
from the supply line will show up at the output of the regulator. This is mainly
caused by both the feedback loop gain rolling down and capacitors inside the linear
regulator which provides AC signal paths conducting between supply and output.
For PMOS linear regulators, the noise on the power supply line directly shows at
the source of the PMOS power transistor. High PSRR performance can be achieved
by making the gate node have the same variation with source node. Therefore, the
VSG is unchanged. For NMOS linear regulator design, the signal conducting path
from the power supply to the power transistor gate should be minimized. In this way,
the VGS of NMOS power transistor is not affected by the noisy power supply.
2.4.2
Output Noise
The output noise is an important specification when the linear regulator is loading
a noise sensitive Analog/RF block, for example a high quality audio circuit or a RF
transceiver. The noise coming from the linear regulator will degrade the loading
circuit performance. The noise of a linear regulator consists of three main parts:
band-gap reference noise, feedback elements noise, linear regulator circuit noise.
VIN
Vn,bg Vn,fb Vn,regulator
Linear
Regulator
Circuit
Bandgap
VOUT
Z1
Vfb
Z2
Figure 2.9: Equivalent input noise of linear regulator.
The equivalent input noise source is shown in Figure 2.9, where Vn,bg is the equivalent output noise from band-gap, Vn,f b is the equivalent noise source from feedback
18
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
elements, Vn,LDO is the equivalent input noise from the linear regulator. The Vn,bg
and Vn,LDO depend on the circuit implementation of band-gap and linear regulator
respectively. If the feedback elements are all resistors, this voltage to voltage feedback
topology in Figure 2.9 has an equivalent thermal noise source contributed by R1 and
2
R2 in parallel [10], which is Vn,f
b =4KT(R1 R2 ).
2.4.3
Electromagnetic Interference
The electromagnetic interference (EMI) of a linear regulator can be defined as the
electromagnetic emissions from the regulator to the main power distribution system [11]. An EMI disturbance example in an automotive environment is illustrated
in Figure 2.10.
Generally, if the pass transistor operates in the saturation region, the PMOS linear
regulator has a better EMI performance, for the reason that the voltage variance
at the regulator output node showing at the power supply line is attenuated by the
output impedance of the PMOS transistor. While for NMOS pass device, at high load
current, the impedance seen from the output node to the supply line may be smaller
than the PMOS output impedance, which may lead to worse EMI performance. It
should be noted that if the pass transistor operates in the linear region, the EMI
performance of NMOS and PMOS regulators should be identical, because the pass
transistor is simply equivalent to a resistor.
Power
Source
Power
Mangement
Unit
Car
Audio
System
Power
Mangement
Unit
Sensors
Linear
Regularor
Digital
Blocks
Figure 2.10: EMI example in automotive environment.
2.5
Frequency Behavior
A linear regulator is a negative feedback system. Therefore, its frequency behavior
determines the loop response time, which is strongly linked to dynamic specifications such as line and load response of the regulator. A critical issue for a feedback
system is stability. Frequency behavior difference between PMOS and NMOS regulators affects the frequency compensation choice. Simple second-order linear regulator
19
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
topologies are shown in Figure 2.11. It must be noted that Figure 2.11 only represents
conventional linear regulators with relatively large CL 5 . The aim of this section is
to illustrate internal pole P1 and output pole P2 movement at low/full current load
scenario.
VIN
Vref
Vref
P1
MP
Gm
ROTA
VIN
P2
Gm
P1
MN
VOUT
Cgate
Iload
ROTA
P2
VOUT
Cgate
R1
Iload
R1
CL
CL
RL
R2
RL
R2
(a)
(b)
Figure 2.11: A simple topology of (a) PMOS regulator (b) NMOS regulator.
Gain(dB)
low current load
full current load
Gain(dB)
P2
low current load
full current load
P1
P2
,
P2
P1
,
P2
Freq(Hz)
Freq(Hz)
(a)
(b)
Figure 2.12: Bode plot of (a) PMOS regulator (b) NMOS regulator.
For PMOS linear regulator shown in Figure 2.11(a), the second-order system consists of two poles P1 and P2 . A possible open-loop bode plot at low load current
5
For some linear regulators, the output capacitive load is very small, therefore their frequency
behavior can not be represented by Figure 2.12.
20
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
scenario is shown by the solid line in Figure 2.12(a). Roughly speaking, P1 is generated by MP gate capacitance Cgate and the Gm stage output resistance ROT A , which
locates at:
fP 1 = −
1
2πROT A Cgate
(2.14)
P2 is generated by the output capacitor CL and regulator load resistance RL ,
which locates at:
fP 2 = −
1
Iload
=−
2πRL CL
2πVout CL
(2.15)
It is clear that as the load current Iload increases, P2 linearly goes to the higher
frequency. The open-loop gain (neglecting the feedback factor) of the PMOS linear
regulator is mainly the multiplication of gain of Gm stage and gain of power transistor,
which is:
Av = Gm ROT A gmp ro
(2.16)
gmp is the transconductance of PMOS power transistor,
β is the current factor
√
which equals to μp Cox W/L. Substituting with gmp = 2βIload and ro ≈ 1/(λIload ),
Equation 2.16 can be rewritten as:
√
Gm ROT A 2β 1
√
Av =
(2.17)
λ
Iload
Suppose Gm and ROT A are unchanged during load current variation, β and λ are
determined by process and transistor size, the open-loop gain is inversely proportional
to square root of loading current Iload . As Iload goes up, the open-loop gain reduces.
A possible second-order NMOS linear regulator topology is shown in Figure 2.11(b).
Again, if CL is in a large value, the possible open-loop bode plot at low load current
scenario is shown by the solid line in Figure 2.12(b). P1 is at the output of OTA
which locates at:
fP 1 = −
1
2πROT A Cgate
(2.18)
P2 is at the output of linear regulator, the output resistance of this node is roughly
1/gmn (assume (1/gmn )RL (R1 +R2 )), where gmn is the transconductance of NMOS
power transistor. The frequency of P2 can be expressed as:
√
2βIload
gmn
fP 2 = −
=−
(2.19)
2πCL
2πCL
From Equation 2.19, P2 is proportional to the square root of load current. As the
load current increases, P2 goes to the higher frequency.
The open-loop gain of NMOS linear regulator is composed by the gain from OTA
and the gain of NMOS power transistor. Assume RL R1 +R2 , it can be written as:
21
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
Av = Gm ROT A
gmn RL
1 + gmn RL
(2.20)
If gmn RL 1, then Av ≈ Gm ROT A . The gmn RL relation can be expressed as:
√
Vout
2βVout
gmn RL = 2βIload
= √
(2.21)
Iload
Iload
Normally, if Iload in hundreds of mA current range, gmn RL could be a term alway larger than 1. For example, Vout =5V, Iload,max =120mA, β ≈1.7, the minimum
gmn RL ≈ 27, which makes the gain of the NMOS source follower roughly equals to 1.
It should be mentioned that from Equation 2.21, as Iload increases, gmn RL reduces,
which makes overall open-loop gain Av also reduce. However, since gmn RL is normally
the dominate term at both numerator and denominator in Equation 2.20, the gain
reduction due to output current increase is negligible.
It is obvious that both the PMOS and NMOS linear regulator in Figure 2.12 are
unstable feedback systems. Therefore, compensation techniques should be applied.
The movement of P2 according to different load current adds difficulty for compensation, for the reason that the compensation scheme should be effective among P2
movement range. Based on Equation 2.15 and Equation 2.19, Figure 2.13 is plotted to
show the frequency range that P2 moves over the loading current from 10μA to 120mA
for PMOS and NMOS regulators respectively. Assume β=1.7, λ=0.2, CL =220nF, it
can be seen that for PMOS regulator, P2 starts at 1Hz and ends around 10kHz. While
for NMOS regulator, P2 starts at 5KHz and ends at 500kHz approximately.
6
10
P2 PMOS regulator
P NMOS regulator
5
P2 Frequency(Hz)
10
2
4
10
3
10
2
10
λ=0.2
β=1.7
CL=220nF
1
10
0
10 −5
10
−4
10
−3
−2
10
10
Output Current(A)
−1
10
0
10
Figure 2.13: P2 movement over load current.
It can be concluded that the P2 movement range for NMOS linear regulator is
much wider than the PMOS one. For PMOS linear regulators, the P2 movement can
be controlled within the bandwidth (e.g. keep the bandwidth greater than 10kHz),
22
CHAPTER 2. COMPARISON OF NMOS AND PMOS LINEAR REGULATORS
therefore the number of poles and zeros within bandwidth can be unchanged during
load current variation, which may provide better chance for compensation. While
for NMOS linear regulators, wide P2 movement may go out of the bandwidth, which
adds more complexity for compensation.
23
Chapter 3
Design of NMOS Linear Voltage
Regulator
3.1
Pass Device Characteristic and Sizing
Before really entering into the design phase of the NMOS linear regulator, both pass
transistor characteristic and its sizing should be known. As stated in Section 1.4,
the maximum supply voltage is 40V, therefore a power transistor with a high breakdown voltage should be used. A double diffused n-type MOSFET in advanced BCD
technology [12] is shown in Figure 3.1, the source of the transistor is implanted in a
p-well. The n-well is acting as the drift region. p-well and n-well are forming a PN
diode which is the body diode. The transistor is based on silicon on insulator (SOI)
technology. The buried oxide is used to isolate the substrate.
D
S
G
p+ n+
Pwell
G
D
isolation
n+
Nwell
Buried oxide(BOX)
Substrate
S
Figure 3.1: Power MOS symbol and the cross section view.
The minimum width to length ratio of the power transistor needs to be determined.
The pass transistor should work in saturation region and linear region. In saturation
region, the drain current ID and VGS relation is quadratic, while in linear region this
relation is linear. For the same VGS range, the current conduction ability bottleneck
is in linear region. Therefore, the power transistor minimum width to length ratio can
be found by measuring the linear region drain-source resistance RDS . In this design,
the expected RDS is 0.5V/120mA≈4.17Ω.
24
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Practically, the minimum width to length ratio should be enlarged to compensate
non-idealities such as bond wire resistance, transistor mismatch, etc. Moreover, the
heat density should also be taken into account before finally deciding the area of the
transistor. Finally, a NMOS power transistor with an area three times smaller than
the PMOS power transistor (used in the available PMOS linear regulator) is chosen
in this design.
3.2
NMOS Linear Regulator Topology
From top level point of view, if starting from a PMOS linear regulator topology to
design its NMOS equivalent, an analog level shifter block should be added to level up
the gate voltage as shown in Figure 3.2. It should be mentioned that the op-amp is
built in low voltage domain (VDDL ) in the previous PMOS design on considerations
of better transistor matching1 and smaller silicon area. The charge pump is added
to boost the level shifter supply voltage when the battery (VBAT ) is low (regulator
in low drop-out). When the battery is high, the charge pump is disabled and the
battery is supplying the analog level shifter.
VBAT
VDDL
VREF
Op-amp
Charge
Pump
Analog
Level
Shifter
VBAT
MN
Figure 3.2: NMOS linear regulator topology.
There are three blocks in this NMOS linear regulator top view (op-amp, analog
level shifter, charge pump), it is easy to find ways to combine some blocks together.
For example, the charge pump and analog level shifter can be combined which directly
boost the op-amp output voltage up to control the gate of MN . Giustolisi et al. are
using charge merging technique to boost the gate voltage [13][14]. Camacho et al. are
1
High voltage transistors are normally with poor matching characteristics
25
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
applying a switched floating capacitor to generate the gate voltage [15]. The charge
pump and analog level shifter combining together has advantages in aspect of lower
static current consumption and less complexity of the circuit. The biggest disadvantage is the noise that the switching floating capacitor circuit generates. According to
the application environment for this design, the NMOS regulator is in low drop-out
regulation (LDO mode) only during engining starting. In most of operation time,
the linear regulator is working in high drop-out regulation (HDO mode), the switch
circuit still adds noise in high drop-out region, which is a drawback for automotive
applications.
The other method to simplify Figure 3.2 is to combine the charge pump and the
amplifier together (neglecting the analog level shifter stage) [16]. The advantage of
this combination is that the charge pump is effective only during the low battery case.
The switching noise exists in low battery supply, which only lasts for a short period
of time. In normal case, the amplifier is directly connected to battery. As the battery
voltage can be maximum 40V, a high voltage amplifier should be designed.
3.3
High Voltage Error Amplifier
Both operational transconductance amplifier (OTA) and operational amplifier (opamp) can be used as a gain stage in linear regulator design. The gain stage is also
named as “error amplifier (EA)”, because it amplifies the voltage difference between
the reference and the feedback voltage. As discussed in Section 2.2 and Section 2.3,
the error amplifier characteristics are directly related to the static and dynamic performance of a linear regulator. Therefore, the design of error amplifier is key of the
whole linear regulator design.
Since OTA has a high output resistance, its output resistance and power transistor
gate capacitance can be combined together to form a dominate low frequency pole,
which is referred to as internal compensated regulator2 . This is a good solution
for some capacitor-free linear regulator structures [17][18]. For these structures, the
low output capacitance leads to a high frequency output pole (outside the desired
bandwidth), the system can be designed as a single pole system.
For external compensated linear regulators (the output pole is the dominate one),
an op-amp (cascading of an OTA and a buffer) is common to drive the gate of the
power transistor. Since the output pole is the dominate one, any internal poles will
add difficulties for compensation. Therefore, a buffer is added between the OTA and
the gate of power transistor. This configuration makes the power transistor gate node
with low impedance (for the low output resistance of the buffer). The OTA and the
buffer interface is also with low impedance (for the low parasitic capacitance between
OTA and buffer). In this way, one low frequency pole at the power transistor gate
(OTA as gain stage) is traded by two relative high frequency poles (op-amp as gain
stage).
2
The dominated pole is inside the control circuit
26
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
VBAT or VCP
M1
M9
M8
M10
M7
M11
Cgate
VDDL
M6
M2
low
voltage Vin+
domain
M5
M3
VB2
Vin-
M4
GND
OTA
Buffer
Figure 3.3: High voltage operational amplifier with cascode low voltage input pair.
In this design, the op-amp is preferred to drive the gate node of the power transistor. This preference is mainly based on the frequency compensation choice which
will be discussed in Section 3.4.3. The high voltage operational amplifier is shown
in Figure 3.3. The input pair transistors (M3 and M5 ) are low voltage transistors
for better matching. The gain stage is composed by transistors M1 -M9 , two diode
connected transistors M7 and M8 are mirroring the current flow through their branch
to M10 and M11 .
M10 and M11 is named as a feed-forward Class AB biasing output stage [19]. The
drawback of this topology is the output voltage swing is limited by the gate-source
voltage of the output transistors [20]. However, in this design, considering the supply
is provided either by the charge pump or the battery (always higher than 10V), the
output voltage swing of the op-amp can be designed within 5.5V∼8.3V, which means
the requirement of op-amp output voltage swing is not critical.
One consideration of using a Class AB output stage is during line and load transient variation, the capacitative nodes may slew. The overall slew rate is limited by
large capacitive nodes. By applying this Class AB output stage, the slew rate at the
gate node can be increased.
27
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
3.4
Frequency Compensation
For now, the size of the power transistor, regulator topology and op-amp structure
are decided, the next step is to tie these modules into a feedback loop. As discussed in
Section 2.5, the NMOS linear regulator is difficult to compensate because the output
pole movement over load current is dramatic. In this section, firstly the load capacitor
size of this linear regulator is chosen, then the feedback loop is modeled in small signal
domain. Finally, the proposed frequency compensation will be presented.
3.4.1
Output Capacitor Sizing
In this design, the external output capacitor is required as this linear regulator is
targeted for providing supply voltage to devices on printed circuit board (PCB).
From previous PMOS linear regulator design, a typical value 2.2μF external ceramic
capacitor is defined. Since the NMOS regulator has possible advantages in transient
response, there might be chance to reduce this output external capacitance in order
to reduce the linear regulator cost. An output ceramic capacitor of 220nF is targeted
in this design.
However, it should be noted that the value of output capacitor is related to high
frequency performance such as PSRR, noise, etc. Lowering the output capacitance
value may degrade these performance. Another challenge of reducing the output
capacitance is the smaller output capacitance, the wider frequency range the output
pole moves as expressed in Equation 2.19, which may add difficulties for frequency
compensation.
3.4.2
Small Signal Modeling
Before doing frequency compensation, the small signal behavior of the feedback loop
should be modeled. Based on the high voltage op-amp structure and linear regulator topology, the small signal equivalent of the feedback loop can be expressed in
Figure 3.4.
It should be noted that the Class AB output stage is modeled as a single source
follower. In numerical calculation, the gm,BU F is the transconductance of p-type and
n-type source followers (M10 and M11 in Figure 3.3) adding together. The gate-source
capacitance of M10 and M11 are neglected.
The transconductance of the power transistor (gm,M N ) is varying over different
load current, which changes the small signal behavior of the loop. It is necessary
to model the transconductance of the power transistor MN first. Transconductance
modeling of NMOS power transistor is based on two different operating regions.
In sub-threshold region (IL is low), the n-channel of MN is not formed. The
gate voltage is controlling the p-type substrate to form a NPN bipolar transistor.
Therefore, the transconductance of the NMOS transistor can be roughly modeled
as a bipolar junction transistor (BJT). The transconductance of BJT is expressed
28
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
VBAT
OTA
MN
BUF
Vref
R1
CL
RL
R2
Small Signal Equivalent
GM,OTA
gm,BUF
ROTA
COTA
Cgd,MN
Cgs,MN
gm,MN
R1
CL
RL
R2
Figure 3.4: Small signal equivalent of NMOS linear regulator.
in Equation 3.1, where Vt is the thermal voltage, Iq is the quiescent current, n is a
constant.
IL + Iq
(3.1)
nVt
In saturation region, the transconductance of NMOS power transistor can be modeled as Equation 3.2, where μn is electron mobility, Cox is the gate oxide capacitance,
W and L are the width and length of the power transistor, VGS is the gate to source
voltage, VT H is the threshold voltage.
W
W
(3.2)
gm,saturation ≈ μn Cox (VGS − VT H ) = 2μn Cox IL
L
L
gm,substhreshold ≈
29
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
For now, the transconductance of each transistor operation region is modeled. In
this design, the current factor β = μn Cox W
≈ 1.7. The transconductance is plotted
L
in Figure 3.5. The solid line is the simulation result from Spectre, the dashed line is
from the calculation results based on Equation 3.1 and Equation 3.2. (Matlab code
is shown in Appendix C.1)
0
10
Simulated
Calculated
−1
10
Gm(A/V)
−2
10
−3
10
−4
10
Linear Region
Saturation Region
−5
10 −6
10
−4
10
−2
IDrain(A)
10
0
10
Figure 3.5: Transconductance of NMOS power transistor.
The symbolic transfer function of Figure 3.4 need to be calculated. First of all,
the AC feedback loop is broke at the negative input of the op-amp while keeping the
DC bias point right as shown in Figure 3.63 .
The transfer function is calculated as the signal transferring from Vin to Vout . At
each node(V1 -V3 ) the current follows Kirchhoff law. Then, there are equations as
follows:
⎧
ROT A
⎪
⎪
−Vin GM,OT A
= V1
⎪
⎪
1 + sROT A COT A
⎪
⎪
⎪
⎪
⎪
⎨ (V1 − V2 )gm,BU F = sCgd,M N V2 + sCgs,M N (V2 − V3 )
RL
(3.3)
(V2 − V3 )(gm,BU F + sCgs,M N )
= V3
⎪
⎪
⎪
1
+
sR
C
L L
⎪
⎪
⎪
⎪
R
2
⎪
⎪
V3
⎩ Vout =
R1 + R2
There are 4 equations and 4 unknown symbolics (suppose input signal Vin is
already known) in Equation 3.3. The relation between Vin and Vout can be calculated
3
In this design, the feedback loop is broke by Spectre stb analysis with the method presented in
[21]
30
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
V1
GM,OTA
gm,BUF
COTA
ROTA
Cgd,MN
V2
Cgs,MN
gm,MN
V3
R1
CL
Vout
Vin
RL
R2
Figure 3.6: Transfer function calculation.
in Matlab (see Appendix C.2), the solution can be simplified based on the practical
component parameters (Table 3.1):
Table 3.1: Components Parameters of the NMOS Linear Regulator
Symbol Parameter Symbol Parameter
R1
6.26MΩ
CL
220nF
R2
2MΩ
COT A
0.3pF
gm,BU F
90μS
gM,M N
60mS
GM,OT A
59μS
Cgs,M N
14pF
ROT A
1.31GΩ
Cgd,M N
8pF
The transfer function can be written as:
Vout
gm,M N gm,BU F GM,OT A R2 RL ROT A + sgm,BU F Cgs,M N GM,OT A R2 RL ROT A
(3.4)
≈
Vin
s3 CL COT A (Cgd,M N + Cgs,M N )(R1 + R2 )RL ROT A
+s2 gm,BU F CL COT A (R1 + R2 )RL ROT A
+sgm,M N gm,BU F COT A (R1 + R2 )RL ROT A
+gm,BU F (R1 + R2 )(1 + gm,M N RL )
Equation 3.4 can be further simplified as (suppose the poles are widely separated,
the detailed simplification steps are discussed in Appendix A):
Vout
Vin
Cgs,M N
gm,M N
≈ Av
Cgs,M N + Cgd,M N
CL
(1 + sROT A COT A )(1 + s
)(1 + s
)
gm,BU F
gm,M N
1+s
31
(3.5)
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
R2
gm,M N RL
.
R1 + R2 1 + gm,M N RL
From Equation 3.5, there are three poles and one zero in the transfer function. The
zero Z1 is formed by the power transistor gm,M N and Cgs,M N , which is a feed-forward
zero locates at the left half plane (LHP), the frequency of it is:
where Av is the DC gain of the loop, Av = −GM,OT A ROT A
Z1 = −
gm,M N
2πCgs,M N
(3.6)
Pole P1 is generated by the interface of the OTA and the buffer, the frequency is:
1
P1 = −
(3.7)
2πROT A COT A
Pole P2 is formed by the buffer output resistance and the power transistor gate capacitance, it is at relative high frequency for the buffer output resistance is 1/gm,BU F ,
the frequency is:
P2 = −
gm,BU F
2π(Cgs,M N + Cgd,M N )
(3.8)
Pole P3 is generated by the output capacitance CL and the gm,M N . The resistance
seen from the regulator output node is roughly 1/gm,M N , the frequency of P3 is:
P3 = −
3.4.3
gm,M N
2πCL
(3.9)
Proposed Compensation Scheme
As discussed in Section 3.4.2, the transfer function of the feedback loop has three
poles (P1 -P3 ) and one zero (Z1 ). P1 and P2 are fixed at certain frequencies, Z1 and
P3 are variant to load current due to gm,M N is in their expressions. Since Z1 is a high
frequency LHP zero, it increases both gain and phase at a certain frequency range
and possibly makes the feedback loop more stable. The only “trouble maker” to the
stability of the loop is the output pole P3 , because it can vary a lot over the whole
output current range (Figure 2.13).
The compensation scheme should accommodate the P3 movement. In other words,
the compensation should be functional over all current load. The wide movement
range of P3 adds difficulties for compensation. To deal with this movement, roughly
speaking, two methods might be effective:
(1) Making P3 always out of the expected bandwidth.
(2) Accommodate P3 movement by adding a zero.
Method (1) can be realized by increasing the standby load current (e.g. in mA
range) to move P3 to higher frequency, but this is unacceptable for the low quiescent
current requirement in this design. It can also be realized by some pole-splitting
methods [7][22], which push the output pole out of the bandwidth. However, two
reasons make this solution not suitable for this design. One is the gain of NMOS
32
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
power transistor in source follower configuration is near 1 which makes pole spitting
very difficult. The other is the large 220nF load capacitor resulting the output pole
at relatively low frequency. To push this pole to the higher frequency may require a
very large spitting capacitor and high current consumption.
Gain(dB)
low current load
full current load
P1
P3
,
P3
Zc
Zc
0
Freq(Hz)
Figure 3.7: Compensation scheme of Method (2).
Method (2) can be conceptually shown in Figure 3.7, where Zc is the zero added in
the loop. It can be seen that as the load current increases, the output pole P3 moves to
the higher frequency. However, due to the existence of Zc , the loop is stable because
the phase shift of P1 is compensated by Zc . It is interesting to notice that as P3 goes
to higher frequency, the bandwidth also get extended. This may add advantages on
transient performance as the bandwidth of the linear regulator is playing a role in
line/load response.
It seems that Method (2) is a good candidate for the frequency compensation.
To compensate this loop, the zero Zc should meet two requirements: One is it must
near the minimum frequency of P3 to ensure the low current load stability; the other
requirement is the associated pole generated by adding zero Zc should be outside the
maximum close-loop bandwidth. The drawback of Method (2) is the generation of low
frequency Zc needs large passive components (big resistor and big capacitor), which
requires large silicon area. Also, adding Zc through passive components will bring an
associate pole with it. A few zero generation topologies are shown in Figure 3.8. If
the Zc is at low frequency, the associated pole is also at relatively low frequency.
To make Zc located at low frequency without consuming too much silicon area,
the resistive divider R1 and R2 in Figure 3.4 is preferred to be reused in frequency
compensation as shown in Figure 3.8(c), because the low quiescent current requires
large R1 and R2 (e.g. in MΩ range). To make the associate pole locate at higher
frequency, literature [23] presents an active zero compensation scheme, which is able
to generate a zero by using the resistive divider. Two drawbacks in this solution
are unacceptable for this design, which are: (1) the interface between the active zero
generation circuit and the resistive divider are adding DC inaccuracy at the output;
33
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Cz
Rz
Rz
R1
R1
Cz
C1
C1
C1
C2
R1
ωZc=1/RzCz
ωpole1=1/R1Cz
ωZc=1/RzCz
R2
ωZc=1/R1C1
ωpole1=(1/RzCz)(1+Cz(1/C1+1/C2))
ωpole1=1/(R1||R2)C1
ωpole2=1/RzC1
(a)
(b)
(c)
Figure 3.8: Adding a zero and its associated pole.
(2) the active zero generation circuit may not be functional when the output voltage
varies vigorously.
By analyzing the structure shown in Figure 3.8(c), it can be calculated that the
frequency of the associated pole is (R1 + R2 )/R2 times higher than the zero. The
optimum solution for this design is making the associated pole absolutely disappear.
A possible solution can be to make the associated pole merge with other poles. To
be specific, by making the dominate pole at the output of the resistive divider, the
time constant of the associated pole can be added into the very large time constant
generated by the dominate pole. This idea is illustrated in Figure 3.9.
Vin
R1
C1
Vout
Cbig
R2
Figure 3.9: Adding a zero while merging the associated pole with dominate pole.
The transfer function from Vin to Vout in Figure 3.9 can be written as:
34
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Vout
Vin
R2
R2 (1 + sR1 C1 )
1 + sR2 Cbig
=
=
R1
R2
(R1 + R2 ) + sR1 R2 (Cbig + C1 )
+
1 + sR1 C1 1 + sR2 Cbig
(3.10)
The pole is at −1/2π(R1 ||R2 )(Cbig + C1 ) and the zero is at −1/2πR1 C1 . If Cbig C1 , the effect of the associated pole on the dominate pole is negligible.
For now, the method of adding a zero without being troubled by its associated pole
is found. The next step is to generate a large capacitance to form the Cbig . It turns
out that pole splitting technique is a perfect candidate for generating an equivalent
large capacitance. In this design, the Cbig can be generated by connecting the high
voltage op amp into an integrator configuration by C2 as shown in Figure 3.10. The
equivalent capacitance at the input of amplifier is around Av C2 , where Av is the
open-loop gain of the op-amp. If the signal transfers from the input node of resistive
divider Vin to the gate node of power transistor Vgate , the nodal equations can be
written as:
⎧
Vin − V1
V1
⎪
⎪
+ s(Vin − V1 )C1 =
+ s(V1 − Vgate )C2
⎪
⎪
R1
R2
⎪
⎪
⎨
V2
(3.11)
−GM,OT A V1 =
+ sCOT A V2
⎪
R
OT
A
⎪
⎪
⎪
⎪
⎪
⎩ gm,BU F V2 = gm,BU F Vgate + sCgate Vgate + s(Vgate − V1 )C2
Suppose the poles and zeros are separated, transfer function is calculated by Matlab (Appendix C.3) as4 :
Vgate
Vin
s3 C1 C2 COT A R1 R2 ROT A + s2 C2 COT A R2 ROT A
−sgm,BU F C1 GM,OT A R1 R2 ROT A − gm,BU F GM,OT A R2 ROT A
≈ 3
s C1 COT A Cgate R1 R2 ROT A + s2 gm,BU F C1 COT A R1 R2 ROT A
+sgm,BU F C2 GM,OT A R1 R2 + (R1 + R2 )gm,BU F
(3.12)
The transfer function can be further simplified as:
Vgate
Vin
C2 COT A
C2 COT A
− s2
)
gm,BU F R1 C1 GM,OT A
gm,BU F GM,OT A
≈ Av
COT A C1
Cgate
[1 + sGM,OT A ROT A C2 (R1 ||R2 )](1 + s
)(1 + s
)
GM,OT A C2
gm,BU F
(1 + sR1 C1 )(1 − s
where Av = −GM,OT A ROT A
(3.13)
R2
R 1 + R2
4
The simplification is based on C1 =10pF, C2 =1.2pF and other numerical values shown in Table 3.1
35
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
V2
GM,OTA
Vgate
BUF
MN
Cgate
COTA1/gm,BUF
ROTA
C2
C1
V1
Vin
R1
R2
Figure 3.10: Integrator configuration with C2 .
First starting from the numerator, there are three zeros, the first zero Z1 is the
expected zero to compensate the system, which locates at:
1
(3.14)
2πR1 C1
Another two zeros are generated by the feed-forward capacitor C2 . It should be
noted that this zero pair is a LHP zero and a RHP zero in combination. The content
in the numerator second parentheses of Equation 3.13 can be simplified as (based on
R1 C1 C2 COT A ):
Z1 = −
1 − s2
C2 COT A
GM,OT A gm,BU F
(3.15)
It results two zeros at:
1 GM,OT A gm,BU F
Z2,3 ≈ ±
(3.16)
2π
C2 COT A
We now calculate the pole frequencies, P1 is the pole formed by the splitting
equivalent capacitor C2 and resistive divider, which is at:
P1 = −
1
2πGM,OT A ROT A C2 (R1 ||R2 )
(3.17)
P2 is formed by the OTA transconductance and capacitance, C1 and C2 is forming
a capacitive feedback around the OTA. The pole frequency is:
P2 = −
1 C2 GM,OT A
2π C1 COT A
36
(3.18)
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
P3 is formed by the buffer output resistance and gate capacitance at the power
transistor, which locates at:
P3 = −
gm,BU F
2πCgate
(3.19)
In Equation 3.13, the simplification is based on the assumption that P2 and P3
are separated. P2 and P3 can also form a pair of complex poles. To further model
this transfer function, the transfer function of Equation 3.13 can be written as:
C2 COT A
C2 COT A
− s2
)
Vout
R1 C1 GM,OT A gm, BU F
GM,OT A gm,BU F
≈ Av
C1 COT A Cgate
COT A C1
Vin
[1 + sGM,OT A ROT A C2 (R1 ||R2 )](1 + s
+ s2
)
GM,OT A C2
gm,BU F GM,OT A C2
(3.20)
The complex poles can be formed if:
(1 + sR1 C1 )(1 − s
(
C1 COT A Cgate
COT A C1 2
) <4
GM,OT A C2
gm,BU F GM,OT A C2
(3.21)
gm,BU F
C2 GM,OT A
<4
Cgate
C1 COT A
(3.22)
which is:
The pair of complex poles will have a resonate frequency at:
1 gm,BU F GM,OT A C2
P2,3 = −
2π
C1 COT A Cgate
(3.23)
For now, the signal transfer behavior from the input of the resistive divider to
the gate of power transistor has been analyzed. It would be necessary to know the
total feedback loop transfer function. The signal transfer from the gate of the power
transistor MN to the output of the linear regulator will meet one zero (Equation 3.6)
and one pole (Equation 3.9). Assume Cgate ≈Cgs,M N +Cgd,M N and neglect the resistive
divider loading effect due to break the AC loop (for CL is large), the simplified transfer
function of the whole loop can be written as:
C2 COT A
Cgs,M N
)(1 + s
)
Vout
gm,BU F GM,OT A
gm,M N
≈
C1 COT A Cgate
COT A C1
CL
Vin
[1 + sGM,OT A ROT A C2 (R1 ||R2 )](1 + s
+ s2
)(1 + s
)
GM,OT A C2
gm,BU F GM,OT A C2
gm,M N
(3.24)
R2
where Av = −GM,OT A ROT A
R 1 + R2
Av (1 + sR1 C1 )(1 − s2
The pole zero locations are summarized in Table 3.2.
37
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Table 3.2: Poles and Zeros Location of the Whole Loop
Poles
1
P1 = −
P2,3
Zeros
2πGM,OT A ROT A C2 (R1 ||R2 )
1 gm,BU F GM,OT A C2
≈−
2π
C1 COT A Cgate
P4 = −
Z1 = −
Z2,3
gm,M N
2πCL
1
≈±
2π
Z4 = −
1
2πR1 C1
gm,BU F GM,OT A
C2 COT A
gm,BU F
2πCgs,M N
It should be noted that P2,3 are assumed to be a pair of complex poles (Inequation 3.22 is easily tenable in this design), the P2,3 frequency in the table is the resonant
frequency(where gain and phase reduce on bode plot).
More accurate overall transfer function is calculated by solving nodal equations
which is shown in Appendix B.
The accuracy of the small signal modeling should be verified. Figure 3.11 shows
the low load current bode plot of the overall transfer function, where the solid line
is the Spectre transistor level simulation result. The dashed-dot line is based on the
simplified transfer function shown in Equation 3.24. The dashed line is based on the
calculated overall transfer function Equation B.2 in Appendix B.
It can be seen that the simplified transfer function is accurate enough to describe
transistor level circuit AC behavior. The poles and zeros marked on the figure are
corresponding to Table 3.2.
Since the bode plot at low load current is already known, it would be interesting
to notice the stability. The bode plot can be simplified as shown in Figure 3.12.
Suppose the gain roll down from P1 to P4 is by 20dB/dec, from P4 to 0dB is by
40dB/dec. Then, the following equation holds:
Av,dB − 20log10
fP 4
fBW
− 40log10
=0
fP 1
fP 4
(3.25)
2
fP 4 fBW
fP 1 fP2 4
(3.26)
which is:
Av,dB = 20log10
Suppose the decimal value of Av,dB is Av,decimal , Equation 3.26 can be rewritten
as:
Av,dB = 20log10 Av,decimal = 20log10
which can be simplified as:
38
2
fP 4 fBW
fP 1 fP2 4
(3.27)
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
100
Gain(dB)
Simulated
Calculated
Simplified
P1
50
P4
0
Z1
−50
P2,3
Z4
−100
−150 −4
10
Z2,3
−2
0
10
2
10
4
6
10
10
Frequency(Hz)
10
8
10
10
10
Phase(Degree)
200
Simulated
Calculated
Simplified
150
100
50
0
−50 −4
10
−2
0
10
2
10
4
6
10
10
Frequency(Hz)
10
8
10
10
10
Figure 3.11: Bode plot at IL =0μA.
Av,decimal =
2
fBW
fP 1 fP 4
(3.28)
The bandwidth is:
fBW =
Av,decimal fP 1 fP 4
(3.29)
Since the bandwidth, poles and zeros frequency are already known, the phase
margin (PM) of this bode plot can be written as:
P M = 90 − arctan
fBW
fBW
+ arctan
fP 4
fZ1
(3.30)
which is:
P M = 90 − arctan
Av,decimal fP 1
+ arctan
fP 4
According to Table 3.2, it can be rewritten as:
39
Av,decimal fP 1 fP 4
2
fZ1
(3.31)
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Gain(dB)
P1
Av,dB
20dB/dec
P4
40dB/dec
0
fP1
fP4
fBW
Freq(Hz)
fZ1
Z1
Figure 3.12: Simplified bode plot analysis at IL =0μA.
P M = 90 − arctan
CL
+ arctan
gm,M N R1 C2
gm,M N R1 C12
CL C2
(3.32)
Assume Av,decimal fP 1 is 100kHz, sweep fP 4 and fZ1 , the phase margin can be
plotted in Figure 3.13.
Phase Margin(Degree)
100
80
60
40
PM increase
20
0
1000
0
800
2000
600
f (Hz)
P4
4000
400
6000
200
8000
0
fZ1(Hz)
10000
Figure 3.13: Phase margin analysis at IL =0μA.
40
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
It can be seen that either moving fP 4 to higher frequency or moving fZ1 to lower
frequency will improve the phase margin. However, these two approaches are costly for
the design. To bespecific, moving fP 4 to the higher frequency means more quiescent
current (gm,M N ∝ (Iq + IL )). While moving fZ1 to lower frequency means increasing
R1 C1 , which means more silicon area.
Next, the feedback loop stability at high current load is investigated. Again, the
transfer function is based on Equation B.2 and Equation 3.24. gm,M N is based on
Figure 3.5. The bode plot at full current load (IL =120mA) is shown in Figure 3.14.
The solid line is the transistor level simulation result in Spectre, the dashed line is
the based on the overall transfer function and the dashed-dot line is based on the
simplified transfer function.
100
P
Gain(dB)
50
1
Simulated
Calculated
Simplified
P
4
Z
0
P
1
2,3
−50
Z
4
Z
−100 −4
10
2,3
−2
10
0
10
2
4
10
10
Frequency(Hz)
6
10
8
10
10
10
Phase(Degree)
200
Simulated
Calculated
Simplified
100
0
−100 −4
10
−2
10
0
10
2
4
10
10
Frequency(Hz)
6
10
8
10
10
10
Figure 3.14: Bode plot at full load current IL =120mA.
It can be concluded that the calculated transfer function describes the transistor
level AC behavior accurately. P4 has already moved to the higher frequency, which
resulted in a bandwidth extension. However, as shown in Figure 3.14, the feedback
system at full current load is instable, because the bandwidth is larger than the P2,3
frequency, resulting in four poles one zero inside bandwidth. Since the bandwidth
should be lower than the P2,3 frequency, it is important to know the bandwidth
expression. The simplified bode plot is show in Figure 3.15
Since the frequency axis(x-axis) is in logarithmic scale. The following holds:
41
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
P1
Gain(dB)
Av
P4
Z1
0
fP1
fZ1
fintegrator fP4
fBW
Freq(Hz)
Figure 3.15: Stability analysis at high load current.
fP 4
(3.33)
fintegrator
fZ1
Using the pole-zero expressions in Table 3.2, the bandwidth can be written is:
fBW
=
gm,M N C1
(3.34)
2πCL C2
From Equation 3.34, it can be seen that either reducing C1 or increasing CL and
C2 can limit the bandwidth. However, according to Equation 3.32, the value of C1
is chosen to increase the phase margin at low current load. Typical value of CL is
determined. The only value can be tuned is C2 . As C2 increases, the fBW is limited.
P2,3 also go to the higher frequency which allows us to stabilize the system.
By increasing C2 the system can be compensated by sort of “narrow-banding”
technique, but it sacrifices the transient performance by making the feedback loop
bandwidth slower. If this bandwidth extension characteristic of the proposed compensation scheme can be taken advantage of, methods of pushing P2,3 to higher frequencies without limiting the bandwidth should be considered.
fBW =
3.5
Adaptive Biasing
In this section, an adaptive biasing method is introduced which can stabilize the system without sacrificing the bandwidth. Form Table 3.2, P2,3 can be moved to higher
frequency by increasing gm,BU F and GM,OT A . According to the op-amp topology (Figure 3.3), it can be known that the tail current flow through M4 determines both the
bias current of the OTA and the buffer. As the tail current increase, both the gm,BU F
and GM,OT A will increase. If the tail current of M4 is proportional to the load current
IL , then P2,3 will move to higher frequency as IL increases. In this way, the stability of
the loop can be ensured without sacrificing the bandwidth. The concept of adaptive
biasing is illustrated in Figure 3.16.
42
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
VBAT
VBAT or Vcp
Current
Sensing
Op-amp
MN
Vref
nIL
Ibias
R1
CL
IL
R2
Figure 3.16: Illustration of adaptive biasing idea.
3.5.1
Current Sensing for Adaptive Biasing
The current sensing of NMOS transistor can be achieved by keeping the node voltages
of MN and MN 1 exactly the same as shown in Figure 3.17. The source node voltage
of MN and MN 1 are regulated to the same voltage level, the current sensing can work
precisely.
The only error of this current sensing scheme is due to the mismatch of MN , MN 1
and the finite gain of the OTA. It can be found that when the output current increases,
the regulation loop gain reduces, the sensing error increases. Since the output current
sensing is not required to be very accurate, this error can be tolerated.
It should be noted that in low drop-out regulation, MN and MN 1 are effectively
resistors. The sensing current is still with the same ratio to the current flow through
the pass transistor because the RDS resistance is inversely ratioed. Therefore, the
current sensing scheme in Figure 3.17 works accurately in saturation and linear region.
3.5.2
Frequency Compensation for Current Sensing Loop
Since the regulation loop is used for generating a NMOS current mirror, the stability
of this regulation loop should be taken care of. Moreover, the bandwidth of this loop
is the “bottleneck” of the overall bandwidth of the regulator, because the stability of
the main feedback loop is relies on this adaptive biasing. If the adaptive biasing is
slower than the main loop, it might cause stability problems.
R3 and C3 are added at VOU T 1 node for frequency compensation of the current
sensing loop. This compensation is functional when MN 1 is conducting little current.
At this scenario, VOU T 1 node is actually a high impedance node, and the OTA output
also provides a high impedance node. These two low frequency poles inside the loop
cause stability issues.
43
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
VBAT
VREF
MN1
MN
Compensation
100 : 1
VOUT1
VBAT or VCP
C3
VOUT
Vg12
M12
R3
OTA2
R1
CL
VOUT
IL
M13
M15
VOUT1
M16 M17
Vg12
Isensed
R2
Vbias
M14
M19
M18
GND
OTA2
Figure 3.17: Current sensing scheme with regulated source node voltage.
Normally, to deal with two low frequency poles, “pole splitting” is a good candidate. However, there are two causes that make it not suitable for this design. The
first is the bandwidth of this regulation loop should not be limited by frequency
compensation. The second is at high load current, the gain reduction of M12 (due to
current flow through MN 1 ) will make the spitting not very effective.
Based on these considerations, a compensation scheme which does not limit the
bandwidth and only effective at low current load is desired. The current sensing loop
is broke at the VOU T 1 node. The equivalent small signal model is shown in Figure 3.18,
the transfer function can be written as:
Vin
GM,OTA2
V1
Vout
V2
COTA2
gm12
C3
ro12
ROTA2
1/gm,MN1
Csb,MN1
1/gm13
Figure 3.18: Small signal equivalent of current sensing loop.
44
R3
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
⎧
V1
⎪
⎪
Vin GM,OT A2 =
+ sV1 COT A2
⎪
⎪
ROT A2
⎪
⎪
⎪
⎨ g (V − V ) = g V
m12 1
2
m13 2
Vout
Vout
⎪
⎪
⎪
gm12 (V1 − V2 ) =
+ gm,M N 1 Vout + sCsb,M N 1 Vout +
⎪
1
⎪
ro12
⎪
⎪
R3 +
⎩
sC
(3.35)
3
The complete transfer function is written as:
Vout
GM,OT A2 ROT A2 ro12 (1 + sC3 R3 )
gm12
=
Vin
gm12 + gm13 (1 + sROT A2 COT A2 )[1 + gm,M N 1 ro12 + s(C3 ro12 + ro12 Csb,M N 1
+C3 R3 + gm,M N 1 ro12 C3 R3 ) + s2 C3 R3 ro12 Csb,M N 1 ]
(3.36)
Suppose gm,M N 1 ro12 1, C3 Csb,M N 1 , Equation 3.36 can be simplified as:
GM,OT A2 ROT A2 ro12 (1 + sC3 R3 )
Vout
gm12
≈
Vin
gm12 + gm13 (1 + sROT A2 COT A2 )[gm,M N 1 ro12 + s(1 + gm,M N 1 R3 )ro12 C3
+s2 C3 R3 ro12 Csb,M N 1 ]
(3.37)
It can be seen that in Equation 3.37, there is one pole at P5 = −1/(2πROT A2 COT A2 )
and one zero at Z5 = −1/(2πR3 C3 ). For another two poles in the transfer function,
their frequencies are related to the gm,M N 1 . At low current load, the term in the denominator of Equation 3.37 s(1+gm,M N 1 R3 )ro12 C3 ≈sro12 C3 (for gm,M N 1 is quite small
e.g. 1μS), which leads the two poles P6 =−gm,M N 1 /(2πC3 ) and P7 =−1/(2πR3 Csb,M N 1 )
respectively. The simulated bode plot is shown in Figure 3.19.
45
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
100
Gain(dB)
50
P
5
P6
0
Z5
P7
−50
−100 0
10
2
10
4
10
Frequency(Hz)
6
10
8
10
Phase(Degree)
200
100
0
−100 0
10
2
10
4
10
Frequency(Hz)
6
10
8
10
Figure 3.19: Current sensing loop bode plot at IL = 0μA.
At high load current, the term in the denominator s(1 + gm,M N 1 R3 )ro12 C3 ≈
sro12 C3 gm,M N 1 R3 (for gm,M N 1 is much larger due to current increases, gm,M N 1 R3 1),
the P6 and P7 frequencies are changed to −1/(2πR3 C3 ) and −gm,M N 1 /(2πCsb,M N 1 )
respectively. The Z5 and P6 are canceling each other, the P7 is at relatively high
frequency for Csb,M N 1 is quite small. The simulated bode plot of current sensing at
high current load is shown in Figure 3.20.
Figure 3.21 shows the phase margin and bandwidth over all current load for this
current sensing regulation loop, it can be seen that the bandwidth of this loop is
alway higher than 1MHz. The minimum bandwidth happens at the current is at
250mA5 , which is around 3.5MHz. The bottleneck of the main voltage regulation
loop bandwidth should be lower than this value.
5
It should be noted that the typical maximum current load for this regulator is 120mA, however,
stability should be guaranteed to near 250mA before the current limitation operates.
46
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Gain(dB)
100
50
P5
Z5
P6
0
P7
−50 0
10
2
4
10
10
Frequency(Hz)
6
8
10
10
Phase(Degree)
200
150
100
50 0
10
2
4
10
10
Frequency(Hz)
6
8
10
10
Figure 3.20: Current sensing loop bode plot at IL =120mA.
6
x 10
9
85
Phase Margin
Bandwidth
8
75
7
70
6
65
5
60
4
55
3
50
2
45
−6
10
−4
−2
10
10
Load Current I (A)
Bandwidth(Hz)
Phase Margin(Degree)
80
1
0
10
L
Figure 3.21: Phase margin and bandwidth versus load current for current sensing
loop.
47
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
3.5.3
Adaptive Biasing Current Ratio Consideration
For the adaptive biasing, the ratio between output current IL and high voltage opamp bias current should be defined. It is clear from P2,3 frequency in Table 3.2
that the more bias current, the higher frequency of P2,3 . However, this bias current
degrades the overall current efficiency. Especially, in this design, the bias current can
be provided by a charge pump during low battery mode. Higher current ability for
charge pump requires more silicon area.
At high current load, the bias current should be at its maximum. Theoretically, if
P2,3 are always kept at 3∼4 times higher than the bandwidth frequency. The system
can be kept stable with a good damping behavior. However, the bandwidth of the
linear regulator is not increasing linearly with IL . The bandwidth increases faster
near low current load region. Therefore, an adaptive biasing circuit (composed by
M13 , M14 and Rlimit ) with peak current limitation and fast bias increasing rate near
low current load is used, which is shown in Figure 3.22.
The voltage drop on Rlimit is forcing M14 going into the linear region at high current load. The maximum adaptive bias current can be limited to (Vin+ −VT H,3 )/Rlimit .
The adaptive bias current Idyn,bias versus IL is shown in Figure 3.23.
Simplified OTA
M1
M9
Cload
Vin+
Vin-
M3
M5
Idyn.bias
Rlimit
1:100
IL
VB
M4
M14
Vdyn_bias
M13
GND
Figure 3.22: Adaptive biasing on the main voltage feedback loop stability analysis.
48
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Dyanmic Bias Current Idyn.bias(μA)
70
60
50
40
30
20
10
0
−4
10
−2
10
0
2
10
10
Load Current I (mA)
4
10
L
Figure 3.23: Adaptive biasing current versus load current IL .
3.5.4
Adaptive Biasing Effect on Main Voltage Regulation
Loop
The interesting question for adaptive biasing scheme would be “Does it affect the
linear regulator main voltage regulation loop stability?”. To find this answer, the
effect of adaptive biasing on the op-amp output will be analyzed, which is shown in
Figure 3.22.
It can be seen that there are two paths (dashed and solid line) for the adaptive
biasing signal (the sine-wave). If transistors are perfectly matched and there are no
parasitic poles in the signal transfer paths, the op-amp output should not be affected
by the adaptive biasing signal variation (as shown that the solid and dashed waveform
are canceling each other at Cload node). However, in practical circuits there must be
some asymmetries. To further verify the stability of adaptive biasing loop, the AC
loop is broken at M14 gate node, a test AC signal Vt in is injected, the feedback signal
Vt out is received at the M13 gate node. The open-loop gain (Vt out /Vt in ) plot of the
adaptive feedback loop is shown in Figure 3.24.
The maximum gain of the adaptive biasing loop is less than -20dB. Therefore, the
adaptive biasing loop through the whole regulator can not be treated as a “feedback”
system, because even for a signal injects into the feedback system, there is not strong
enough a signal back. Therefore, stability of this adaptive biasing loop is ensured.
49
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
−20
−40
Gain(dB)
−60
−80
−100
I =5μA
L
−120
I =4mA
L
−140
I =12mA
L
I =40mA
L
−160
IL=120mA
−180 0
10
2
4
10
6
10
10
Frequency(Hz)
8
10
Figure 3.24: Adaptive biasing loop gain plot.
3.5.5
Linear Regulator High Current Load Stability with
Adaptive Biasing
At high current load (IL =120mA), the linear regulator main voltage feedback loop
bode plot with adaptive biasing is shown in Figure 3.25. From this plot, it can be
seen that with the implementation of adaptive biasing, P2,3 is moved to the higher
frequency (compare to Figure 3.14), which ensures the system stability at high current
load.
100
W/O Adaptive Biasing
With Adaptive Biasing
Gain(dB)
50
P
2,3
0
−50
−100 −5
10
0
5
10
10
10
10
Frequency(Hz)
Figure 3.25: Linear regulator high current load bode plot with adaptive biasing
50
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
3.6
Over-current Protection
The linear regulator should have the over-current protection (OCP) ability to protect
itself from overload current damage, because current above limitation may cause
the power transistor heating up which reduces its lifetime and may result in device
failure. In real applications, the over-current scenario could be caused by the over
power demand from the loading circuit. In this case, the linear regulator should
better be kept at some constant output current to drive the loading circuit, this
feature prevents the loaded circuit from resetting if the over power demand only lasts
a short period of time.
The output current IL and the load resistance RL relation is shown in Figure 3.26.
If there is no over-current protection mechanism in the linear regulator, the load
current can be very high when RL is low (as the dashed line shows).
IL
with OCP
w/o OCP
Ilimit=250mA
0
RL
+
Figure 3.26: Current limitation scheme.
When the linear regulator is in OCP mode, the output voltage will linearly reduce
with the load resistance. Therefore, the main voltage regulation of the loop should
be disabled, or else this loop will try its best to regulate the output voltage to 5V.
To disable the main regulation loop, one method has been implemented to force the
input transistor into cut-off region as shown in Figure 3.27. Again, the current sensing
should be added to know the exact output current value6 . The over-current protection
is able to control MOCP . If the output current is below Ilimit , current I2 is near 0,
which adds no effect on the overall loop. If the output current is higher than Ilimit ,
then the over-current control circuit will increase the gate voltage of MOCP , making
the current of M9 flows through MOCP . Then, as the I1 barley equals to zero, M5 can
be treated as operating in cut-off region, the main voltage regulation loop is disabled.
6
It should be noted that the current sensing for OCP is not based on Figure 3.17, because in
that figure M12 and M13 both need voltage headroom to be functional. Since VOU T might be a
low voltage during the current limitation, this current sensing circuit in Figure 3.17 can not work
accurately
51
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
VBAT
VBAT or VCP
M1
M9
Current
Sense
M10
M8
I1
I2
MN
C2
Vbias1
M2
M6
M3
M5
VOUT
M11
M7
R1
C1
VREF
CL
RL
R2
Vbias2
M4
GND
Overcurrent
Control
MOCP
Figure 3.27: Over-current limitation.
The detailed transistor level implementation is shown in Figure 3.28. M15 and M16
form a PMOS current mirror which mirrors out the current ID,N 2 flowing through
MN 2 . M15 is a large transistor to ensure a small VSG,15 . M15 , M16 , M18 and M19
compose a current comparator which compares the difference between ID16 and ID18 .
M17 is acting as a voltage clamp to make sure M18 and M19 can be low voltage
transistors (providing advantage in mismatch).
Since there is DC gain in both current comparator and M21 , when the overcurrent protection circuit operates, it actually forms another regulation loop which
forces input current (ID,N 2 ) equaling to some ratio of input current (IRef,limit ). In
this way, the output current can be regulated to a fixed Ilimit , it is actually a current
regulator being formed in over-current protection.
This current regulator has two stages of amplification, which provides a high
gain to ensure the output current accuracy. The stability of this current regulation
loop should be taken care of. In this design, R5 , C4 , M20 have been added for
frequency compensation. Since M21 is acting as a common source amplifier, pole
spitting technique is considered to be a good way to compensate this system. The
additional capacitance C4 at the gate of M8 should be a small value, or it will introduce
asymmetry for the main feedback loop.
52
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
VBAT
VBAT or VCP
100:1
M1
M15
M9
100:1
I2
I1
VOUT
M11
C2
Vbias1
M2
M3
MN2
MN
M7
VREF
ID,N2
M10
M8
M16
C1
R1
M6
CL
M5
RL
R2
Vbias2
M4
GND
C4 R 5
M17
VREF
IRef,limit
M21
20:1 M20
1:100
M19
M18
GND
Figure 3.28: Over-current limitation schematic.
The simplified loop for stability analysis is shown in Figure 3.29. Roughly speaking, 3 poles and 2 zeros are inside the loop. It should be noted that the gate capacitance of MN is neglected in this simplified loop for the reason that M20 can provide
enough current bias for source follower M10 , then the pole at the gate of MN 2 can be
at high frequency.
Since C4 is acting as a pole splitting capacitor, the frequency of P8 is:
P8 = −
1
2π(ro16 ||ro18 )gm21 (ro21 ||ro9 )C4
(3.38)
Due to the introduced capacitive feedback by C4 , P9 is spitted into relative higher
frequency. Suppose the capacitive to ground at node P8 is roughly Cnode8 ≈ Cgs20 +
Cgs21 + Cdb18 + Cdb16 . Then P9 frequency is at:
53
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
M15
Vbias
M16
M9
M10
P9
MN2
VOUT
GM,N2
Stage
P10 Z6
Z7
R5
CL
C4
RL
P8
M21
M20
IRef,limit
M19
GND
M18
Current Comparison
Figure 3.29: Current limitation simplified loop for stability analysis.
P9 = −
C4
gm21
2πCnode9 (Cnode8 + C4 )
(3.39)
where C4 /(Cnode8 + C4 ) is the feedback factor for the capacitive feedback loop that
C4 introduced.
It is interesting to notice that MN 2 is actually a source degenerated transconductance stage, which transfers the voltage signal into current to the current comparator
input. The degeneration impedance is composed by RL and CL . In this way, the
transconductance can be written as:
GM,N 2 =
gm,M N 2
RL
1 + gm,M N 2
1 + sRL CL
=
gm,M N 2 (1 + sRL CL )
1 + gm,M N 2 RL + sRL CL
(3.40)
As the GM,N 2 is the proportional to the transfer function, then it results a zero
Z6 at:
54
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
Z6 = −
1
2πRL CL
(3.41)
And a pole P10 at:
1 + gm,M N 2 RL
(3.42)
2πRL CL
This zero-pole pair locates at range of several kHz (e.g. RL =10Ω, CL =220nF will
result Z6 =73kHz), it will extend the bandwidth (if the bandwidth> Z6 ), which will
cause instability. This problem is quite difficult to handle, because RL is a variable
which can not be decided, CL is a fixed value. As the OCP operates, the fixed
output current results gm,M N 2 is also a constant. It is true that reducing the gm,M N 2
will make the zero and pole close to each other, however, due to accurate matching
requirements, the MN 2 should be at most 100 times smaller than the main power
transistor MN , gm,M N 2 can not be reduced arbitrarily.
The resistor R5 and capacitor C4 generate a LHP zero to save some phase shift
near the the bandwidth, which frequency is roughly at:
P10 = −
Gain(dB)
Z7 = −
100
80
50
20
−10
−40
−70
P
(3.43)
P
8
9
Z
6
P
10
Z
7
2
10
Phase(Degree)
1
2πR5 C4
200
4
10
Frequency(Hz)
6
10
8
10
100
0
−100
2
10
4
10
Frequency(Hz)
6
10
8
10
Figure 3.30: Current limitation loop bode plot (RL =10Ω).
The bode plot of the over-current protection loop is plotted in Figure 3.30. To
enable the over-current protection loop, a RL =10Ω resistor is loaded.
55
CHAPTER 3. DESIGN OF NMOS LINEAR VOLTAGE REGULATOR
The over-current loop stability over different load resistor RL is shown in Figure 3.31. It can be found that over the resistive load, the over-current control system
is stable.
80
35
70
30
65
25
60
20
55
15
50
10
45
5
40
5
Gain Margin(dB)
Phase Margin(Degree)
75
40
Phase Margin
Gain Margin
0
20
10
15
Load Resistance RL(Ω)
Figure 3.31: Current limitation stability over RL .
The main voltage regulation loop bode plot in OCP mode is shown in Figure 3.32.
It can be seen that as the over-current protection is enabled, the main loop gain is kept
at below 0dB, which shows the main voltage regulation loop is effectively disabled.
0
−20
−40
Gain(dB)
−60
−80
−100
−120
R =17Ω
L
−140
RL=15Ω
−160
R =10Ω
L
−180
−200
0
10
RL=5Ω
2
10
4
10
Frequency(Hz)
6
10
8
10
Figure 3.32: Main voltage regulation loop gain plot over RL .
56
Chapter 4
Performance Evaluations
In this chapter, the performance of NMOS linear regulator will be presented and
summarized. All the simulations are based on the test-benches shown in Appendix D.
4.1
4.1.1
Static Performance
Drop-out Region
From Figure 4.1, it shows that the regulator is functional around 5.2V, which makes
low drop-out regulation available. It should be noted that in the low drop-out range
(e.g. the battery voltage VBAT <10V), the charge pump (VCP ) is assumed to be turned
on to provide supply voltage for the op-amp.
5
4
V
OUT
(V)
4.5
3.5
I =5μA
L
IL=60mA
3
I =120mA
L
3
4
5
6
7
8
VBAT(V)
9
10
11
12
Figure 4.1: VOU T versus VBAT (VCP =10V, typical process corner, temp=27°C).
57
CHAPTER 4. PERFORMANCE EVALUATIONS
4.1.2
Quiescent Current and Current Efficiency
The quiescent current Iq over load current IL is plotted in Figure 4.2. When there
is no load current, the quiescent current is 12μA. At full current load scenario, due
to adaptive biasing Iq becomes 1.31mA. It should be noted that the band-gap circuit
quiescent current is excluded in this figure.
0
10
Iq(mA)
Iq=1.31mA when IL=120mA
−1
10
Iq=12μA when IL=0A
−2
10
0
20
40
60
IL(mA)
80
100
120
Figure 4.2: Iq versus IL (VBAT =12V, typical process corner, temp=27°C).
Since adaptive biasing scheme is used in this design, it is important to know how
much the overall current efficiency (as defined in Equation 4.1) it degrades.
ηcurrent =
Iload
× 100%
Iload + Iq
(4.1)
100
Current Efficiency(%)
90
80
70
60
50
With Adaptive Biasing
Without Adaptive Biasing
40
30
−1
10
0
10
I (mA)
1
10
2
10
L
Figure 4.3: Current efficiency (VBAT =12V, typical process corner, temp=27°C).
58
CHAPTER 4. PERFORMANCE EVALUATIONS
Figure 4.3 shows the current efficiency of this NMOS linear regulator. The dashed
line is the current efficiency without adaptive biasing (Iq is always 12μA). It can be
found that the adaptive biasing scheme degrades the current efficiency. However, the
degradation is not very prominent at low current (below 0.1mA). For IL ≈3mA, the
maximum degradation happens due to the biasing current for the op-amp reaches
its maximum (as shown in Figure 3.23), it only reduces this efficiency by 4%. At
high current load, the majority of Iq is contributed by the 100:1 current mirror in the
current sensing circuit, the degradation of the efficiency is around 1%.
4.1.3
Static Output Voltage Accuracy
The static output voltage accuracy of the linear regulator is presented in this subsection. Figure 4.4 shows the line regulation performance. The line regulation ability is
enhanced by the intrinsic gain of NMOS power transistor as expressed in Equation 2.7,
which makes the output voltage quite accurate in response to different battery voltages.
4.9979
4.9978
Output Voltage(V)
4.9977
Temp= 27°C
4.9976
Temp=−40°C
4.9975
Temp=175°C
4.9974
4.9973
4.9972
4.9971
5
10
15
20
25
VBAT(V)
30
35
40
Figure 4.4: Static line regulation (IL =120mA, typical process corner).
Figure 4.5 shows the load regulation performance. The output voltage becomes
more inaccurate as the load current increases. There are two reasons for this inaccuracy, one is as the current goes up, voltage drop on the modeled 25mΩ bond-wire
parasitic resistor will increase (e.g. 25mΩ×120mA=3mV). The other is the DC gain
of the loop decreases as IL increases (Equation 2.11). However, the gain reduction is
not prominent as shown in Figure 3.25. From Figure 4.5, the maximum inaccuracy
is around 3mV, this is mostly contributed by the bond-wire resistance voltage drop.
In practical cases, the mismatch between transistors and passive components also
contribute to the output voltage inaccuracy. Figure 4.6 shows the monte-carlo sim59
CHAPTER 4. PERFORMANCE EVALUATIONS
5.001
5.0005
Output Voltage(V)
5
4.9995
4.999
4.9985
4.998
Temp= 27°C
Temp=−40°C
4.9975
Temp=175°C
4.997 −2
10
−1
10
0
1
2
10
10
Load Current I (mA)
10
L
Figure 4.5: Static load regulation(VBAT =12V, typical process corner).
ulation results of the output voltage over all process corners and temperature range.
One standard deviation (σ) of output voltage is 11.4mV, for ±3σ range, the output voltage will spread ±34.2mV. This inaccuracy can be solved by trimming of the
feedback resistors during the chip fabrication.
120
Number of Samples(#)
100
Sigma=11.4mV
Mean=5.001V
80
60
40
20
0
4.97
4.98
4.99
V
5
(V)
5.01
5.02
5.03
OUT
Figure 4.6: Ouput voltage spread (VBAT =12V,IL =0,-40°C∼175°C).
60
CHAPTER 4. PERFORMANCE EVALUATIONS
4.2
AC Performance
The main voltage regulation open-loop bode plot over different load current is shown
in Figure 4.7. As the load current increasing, the output pole is moving to higher
frequency. Owing to the added zero and adaptive biasing scheme, the system stability
can be ensured.
100
50
I =240mA
Gain(dB)
L
0
IL=0μA
−50
−100
−150 −2
10
0
10
2
10
4
10
Frequency(Hz)
6
8
10
10
10
10
Phase(Degree)
200
150
I =240mA
L
100
50
I =0μA
0
−50 −2
10
L
0
10
2
10
4
10
Frequency(Hz)
6
10
8
10
10
10
Figure 4.7: Bode plot over different IL .
The phase and gain margin is shown in Figure 4.8. It shows that at zero load
current the phase margin is around 35°. However, as the load current increases to
around 10μA, the phase margin is above 45°. It should be noted that although the
system shows under-damped behavior (for the phase margin is low) in low load current range, the regulator output voltage variation due to load response in this range
is not critical. The reason for that is small current variation can be immediately
compensated by the charge stored on the large external capacitor.
The bandwidth of the overall loop is shown in Figure 4.9. The bandwidth is
increased with the load current IL , which meets the expectation in Section 3.4.3.
This increased bandwidth will reduce the loop response time, which improves the
transient performance of linear regulator.
61
CHAPTER 4. PERFORMANCE EVALUATIONS
100
100
Phase Margin
90
Gain Margin
80
80
70
70
60
60
50
50
40
40
30
30
20
−4
10
−2
0
10
10
Load Current I (mA)
2
Gain Margin(dB)
Phase Margin(Degree)
90
20
10
L
Figure 4.8: Phase and gain margin versus IL
3.5
Bandwidth(MHz)
3
2.5
2
1.5
1
0.5
0
0.01
0.1
1
10
Load Current IL(mA)
100
Figure 4.9: Bandwidth versus IL .
4.3
Dynamic Performance
4.3.1
Line Transient Response
The low battery line transient response is shown in Figure 4.10. In this test-case, the
supply voltage of op-amp is 10V (the charge pump is ON). The dashed line shows the
±3σ range of the VOU T during the line transient variation. This ±3σ range in this
62
CHAPTER 4. PERFORMANCE EVALUATIONS
section means over the full temperature range (-40°C∼175°C), with process corners
and mismatch included, 99.97% samples will have the output variation within the
dashed range.
12V
V
BAT
(V)
12
10
3μs
3μs
8
6
4
230
5.5V
5.5V
240
250
260
270
280
Time(μs)
VOUT(V)
5.1
Typical
± 3σ
5.05
5
4.95
230
240
250
260
270
280
Time(μs)
Figure 4.10: Low battery line transient response (IL =120mA, -40°C∼175°C).
The high voltage line transient response is shown in Figure 4.11. It can be seen
that as the NMOS power transistor goes into saturation region, the VBAT transient
variation on VOU T is greatly reduced.
63
CHAPTER 4. PERFORMANCE EVALUATIONS
VBAT(V)
40
30
40V
3μs
3μs
20
12V
10
75
12V
80
85
90
95
100
105
110
115
Time(μs)
5.06
Typical
± 3σ
(V)
5
OUT
5.02
V
5.04
4.98
4.96
75
80
85
90
95
100
Time(μs)
105
110
115
Figure 4.11: High battery line transient response(IL =120mA, -40°C∼175°C).
4.3.2
Load Transient Response
The load transient response for VBAT =12V is shown in Figure 4.12. It can be found
that for a typical process corner (temp=27°C, no mismatch and process corners), the
VOU T variation is around ±50mV. For ±3σ range, the output voltage can vary around
±100mV.
From Figure 4.8, in low load current region, the system shows under-damped
characteristic. It is necessary to check if this region gives any critical under-damp
behavior to the feedback system. The VOU T variation in response to IL varies from 0
to 100μA in 100ns is shown in Figure 4.13. It can be seen that there is a little underdamped behavior showing up, however, the amplitude of output voltage variation is
not prominent due to low IL .
64
CHAPTER 4. PERFORMANCE EVALUATIONS
150
120mA
I (mA)
100
2μs
L
2μs
50
0
120μA
120μA
400
500
600
700
800 900
Time(μs)
1000 1100 1200 1300
5.1
VOUT(V)
5.05
5
4.95
Typical
± 3σ
4.9
400
500
600
700
800 900
Time(μs)
1000 1100 1200 1300
Figure 4.12: Load transient response (VBAT =12V,-40°C∼175°C).
100μA
L
I (μA)
100
100ns
50
0
4
100ns
0μA
5
0μA
6
7
Time(ms)
8
9
Typical
± 3σ
5.02
5
V
OUT
(V)
5.04
10
4.98
4.96
4
5
6
7
Time(ms)
8
9
10
Figure 4.13: Low current load transient response (VBAT =12V,-40°C∼175°C).
65
CHAPTER 4. PERFORMANCE EVALUATIONS
To make the test-bench match practical load current behavior better, a staircase
load current is applied to this regulator. The output voltage variation is shown in
Figure 4.14.
20mA
120μA
50mA
100
120mA
50mA
20mA
120μA
1μs
1μs
L
I (mA)
150
50
0
0
1μs
1μs
1μs
1μs
2
4
6
8
Time(ms)
10
12
14
5.15
Typical
± 3σ
(V)
5
OUT
5.05
V
5.1
4.95
4.9
0
2
4
6
8
Time(ms)
10
12
14
Figure 4.14: Staircase load transient response (VBAT =12V,-40°C∼175°C).
It should be noted that in some transient test-cases, the required minimum IL
is from zero to some high current load. To deal with this case, a current sink path
should be designed. This is discussed in Appendix E.
4.4
4.4.1
High Frequency Performance
Power Supply Rejection
The power supply rejection is shown in Figure 4.15. The PSRR is around 63dB at
100kHz. The worst case for PSRR is around 37dB.
4.4.2
Output Noise
The output noise of this linear regulator is shown in Figure 4.16. The integrated noise
from 1Hz to 1MHz is 66.4μVRM S . The low frequency noise is mainly contributed by
the resistive divider thermal noise and 1/f noise of the input pair transistors. As
frequency goes higher, the output capacitor also plays a role to attenuate the total
noise.
66
CHAPTER 4. PERFORMANCE EVALUATIONS
−30
I =100μA
L
−40
IL=500μA
I =5mA
L
PSRR(dB)
−50
I =25mA
L
I =120mA
L
−60
−70
−80
−90 0
10
2
10
4
10
Frequency(Hz)
6
8
10
10
Figure 4.15: PSRR over IL (VBAT =12V,typical process corner, 27°C).
20
18
Output Noise(μV/√Hz)
16
14
12
10
8
6
4
2
0 0
10
2
10
4
6
10
10
Frequency(Hz)
8
10
10
10
Figure 4.16: Output noise (IL =20mA,typical process corner, 27°C).
4.5
Over-current Protection Performance
The static load current IL versus load resistor RL plot is shown in Figure 4.17. This
plot meets the expectation shown in Figure 3.26. It can be seen that the limitation
current level can vary with temperature.
The test-bench of the over-current limitation is shown in Appendix D. The output
67
CHAPTER 4. PERFORMANCE EVALUATIONS
0.35
°
Temp=175 C
°
Temp= 27 C
0.3
Temp=−40°C
0.25
IL(A)
0.2
0.15
0.1
0.05
0
0
20
40
60
80
100
R (Ω)
L
Figure 4.17: IL versus RL (VBAT =12V, typical process corner).
resistance is periodically varies from 50Ω to 10Ω with 2μs transition time (Figure D.2).
If the over-current protection is not functional, this will lead to the output current
variation from 100mA to near 500mA. Figure 4.18 shows the effectiveness of the overcurrent protection. The load current is kept around 250mA when 10Ω is loaded.
Due to the bandwidth limitation, the current can beyond the limitation at the very
beginning of the output resistance reduction (e.g. from 50Ω to 10Ω). The protection
circuit will regulate the output current to 250mA within 10μs.
It can be found that the regulating current has some spread (from 221mA to
320mA), this is mainly caused by the current mirror error of M18 and M19 in Figure 3.28. In order to save the quiescent current, IRef,limit should be low (250nA in
this design). Therefore a large current mirror ratio should be used. The low current drives this two transistors in weak inversion region where the (VGS -VT H )-ID has
an exponential relation, this makes the current mirror more inaccurate due to VT H
mismatch.
4.6
Overall Performance Summary
Table 4.1 shows the overall performance summary of this NMOS linear regulator.
68
CHAPTER 4. PERFORMANCE EVALUATIONS
6
R =50Ω
Typical
± 3σ
R =50Ω
R =10Ω
L
L
4
V
OUT
(V)
5
L
3
2
2.5
3
3.5
Time(ms)
4
Typical
± 3σ
600
400
L
I (mA)
4.5
200
0
2.5
3
3.5
Time(ms)
4
4.5
Figure 4.18: Over-current protection transient behavior (VBAT =12V,-40°C∼175°C).
Table 4.1: Overall NMOS Linear Regulator Performance Summary
Symbol
Parameter
Min Typ Max
VIN
Regulator Input Voltage
5.5
–
40
VOUT
Output Voltage
4.9
5.0
5.1
ΔVout load
Dynamic Load Regulation
-2
+2
tstabilized Output Voltage Within 0.5% After Load Step
1
ΔVout line
Dynamic Supply Regulation
-2
+2
Iq
Quiescent Current(IL =0, w/o band-gap)
–
12
–
PSRR
Power Suplly Rejection@100kHz
–
63
–
Vnoise
Output Noise
–
66.4
–
CL
External Capacitance
–
220
–
69
Unit
V
V
%
ms
%
μA
dB
μVRM S
nF
Chapter 5
Scaling Features
As the NMOS linear regulator is already designed, the scaling abilities on external
capacitance and maximum load current should be investigated. In this chapter, the
possible scaling features on this NMOS linear regulator will be discussed.
5.1
External Capacitor Scaling
In this design, the typical value of the external load capacitor CL is 220nF. More CL
values are also acceptable. From Figure 3.13, the low load current stability might be
degraded by the large output capacitor (moving fP 4 lower), however, this degradation
can be tolerable. As we discussed, even the low phase margin at low current load
makes the system under-damped, it can be easily compensated by the charge stored
at the output capacitor, which may not result big output voltage variation.
90
Phase Margin
80
70
IL=0μA
60
IL=120mA
50
40
30
20
10
0
0
0.5
1
1.5
2
2.5
3
Load Capaitance(μF)
Figure 5.1: Phase margin among output capacitor sizing range.
The calculated phase margin over different CL is plotted in Figure 5.1. Clearly,
there is a trade-off between high current load and low current load stability. To be
70
CHAPTER 5. SCALING FEATURES
specific, when CL is low (e.g. less than 60nF), at high current load, the phase margin
is only around 30°. This under-damped behavior at high load current will result
large output voltage variation. When CL is high (e.g. greater than 1μF), at low load
current, the phase margin is around 15°.
In this design, the P2,3 is around 10MHz at maximum current load. If the linear
regulator maximum bandwidth is near this frequency at high load current, the system
is instable. Figure 5.2 shows the expected bandwidth over CL . At CL ≈20nF, the
expected bandwidth is at 10MHz, the whole system is quite under-damped which is
risky to define the linear regulator with this CL value. Therefore, the CL with at least
20nF is required for stability.
8
Bandwidth(Hz)
10
7
10
6
10
Possible
Instability
when C <20nF
L
5
10
0
0.5
1
1.5
2
2.5
3
Load Capaitance(μF)
Figure 5.2: Bandwidth at high current load over CL .
To further investigate the impact of different CL value on the transient behavior,
several CL values are chosen for the load transient simulation. The VOU T variation
for IL goes from low to high is shown in Figure 5.3. It can be seen that the different
CL resulting different damping behavior of VOU T . Lower CL makes the phase margin
lower, the system becomes more under-damped as shown in CL =100nF curve. For
large CL , the system is over damped, the reaction time becomes much longer as shown
in the CL =2.2μF curve.
The load transient behavior for IL varying from high to low over different CL is
shown in Figure 5.4. Higher CL value will make the VOU T overshoot smaller, but due
to the larger capacitance, the VOU T needs more time to decrease to nominal output
voltage (5V).
It should be noted that normally a larger CL will result in a better transient
response for a lower linear voltage regulator. However, in this design the CL is
inversely proportional to the bandwidth, if CL is increased, the reduced loop speed will
also degrade the transient performance. From Figure 5.3 and Figure 5.4, increasing
CL from 100nF to 2.2μF only improved VOU T variation by ±7mV approximately.
71
CHAPTER 5. SCALING FEATURES
150
IL(mA)
120mA
100
0.5μs
50
300μA
0
2399.5
2400
2400.5
2401
Time(μs)
2401.5
5
CL=100nF
C =220nF
VOUT(V)
L
C =470nF
4.98
L
CL=1μF
CL=2.2μF
4.96
4.94
2399.5
2400
2400.5
2401
Time(μs)
2401.5
Figure 5.3: Load transient response (IL increasing) with different CL .
150
100
0.5μs
L
I (mA)
120mA
50
300μA
0
1200
1250
1300
Time(μs)
1350
CL=100nF
CL=220nF
5.04
CL=1μF
5.02
C =2.2μF
V
OUT
(V)
CL=470nF
L
5
1200
1250
1300
Time(μs)
1350
Figure 5.4: Load transient response (IL decreasing) with different CL .
72
CHAPTER 5. SCALING FEATURES
5.2
Load Current Scaling
In this design, the typical maximum output current is 120mA. The load current can
also be scalable. To scale the current, the first consideration is power transistor
sizing. From Section 3.1, the minimum of the transistor size is determined by the
linear region RDS resistance of the power transistor. As the maximum load current
increasing/decreasing n times, the RDS should be reduced/increased by n times, which
leads to the size of power transistor increase/decrease by n times.
The second thing to check is the effect on main loop stability when scaling maximum IL . First, the high current load bandwidth is proportional to the transconductance of power transistor gm,M N . Since the size of the power transistor has changed
by n times, the gm,M N is changed by n times, as expressed in Equation 5.1.
nW
W
gm,M N = 2μn Cox
nIL = n 2μn Cox IL
(5.1)
L
L
To roughly keep the same bandwidth to ensure the stability at high current load,
based on Equation 3.34, CL can be tuned to accommodate the gm,M N scaling. This
means CL should also be n times in response to nIL .
For power transistor changes by n times, the Cgate also changes by n times. If
n > 1, P2,3 (Table 3.2) will move to a lower frequency. This means even the maximum
bandwidth is kept at the same, there is still a potential instability risk. P2,3 can be
kept at the same frequency during scaling by changing gm,BU F by n times. This can
be done by providing a n2 times adaptive biasing current.
For the low current load stability, it is a pity that gm,M N at low current load does
not scale with transistor size as analyzed in Equation 3.1. To keep the same phase
margin at low current load (Equation 3.32), the quiescent current flow through power
transistor at low current load should be changed by n times to accommodate the
modified n times CL .1
To make the factor n into practical values, possible IL scaling factors are summarized in Table 5.1. It should be noted that these values are only leading to a functional
(stable) linear regulator, there is still much room for optimization. Different trade-offs
can be made for specific applications.
Table 5.1:
Scaling Factor
IL
n=0.42
50mA
n=1
120mA
n=2.1
250mA
n=4.2
500mA
n=8.4
1A
Load Current Scaling
CL
Max Idyn.bias
100nF
11μA
220nF
65μA
470nF
286μA
1μF
1.2mA
2.2μF
4.6mA
Iq @IL =0A
9.5μA
12μA
17.5μA
26μA
47μA
The linear regulator in this design is scaled up to maximum 1A current load based
on Tablet 5.1. The load transient behavior is shown in Figure 5.5. It can be seen
1
In this design, the quiescent current flow through power transistor is 5μA when IL =0.
73
CHAPTER 5. SCALING FEATURES
that the linear regulator is stable and shows no under-damp behavior. The bondwire resistance will contribute a lot on voltage drop at high current load (around
1A×25mΩ=25mV).
IL(A)
1
1A
2μs
0.5
0
200
1A
2μs
3mA
300
400
500
600
700
Time(μs)
800
900
1000
800
900
1000
VOUT(V)
5.05
5
4.95
Bondwire I×R voltage drop
4.9
4.85
200
300
400
500
600
700
Time(μs)
Figure 5.5: A 1A linear regulator load transient response.
74
Chapter 6
Conclusions and Future Work
In this thesis, a NMOS linear regulator is presented. The small signal behavior of
the regulation loop has been accurately modeled. Based on the small signal model,
a frequency compensation scheme which can generate a zero without being troubled
by its associated pole is proposed. The effectiveness of the compensation is verified
by both calculation and simulation.
This NMOS linear regulator is able to keep ±2% output voltage accuracy within
-40°C∼175°C. With the implementation of adaptive biasing, the quiescent current of
this linear regulator can vary from 12μA to 1.31mA, the current efficiency is only
degraded within 4%. Owing to the proposed frequency compensation scheme, this
regulator can achieve a maximum 3MHz bandwidth. Compared to the PMOS linear
regulator counterpart, the power transistor area can be decreased by 3 times, the
output external capacitor can be reduced from 2.2μF to 220nF without sacrificing
the performance.
Due to the time limit, measurement results of this NMOS linear regulator testchip is not included in this thesis. Beside the silicon verification of this work, from
design point of view, the future work can be done in four aspects: (1) designing an
area-efficient charge pump which has an output current ability around 200μA; (2)
designing a low battery sensing circuit which can enable/disable the charge pump;
(3) adding short circuit protections, over-voltage protections (e.g. VGS protection)
and ESD protections; (4) trimming can be implemented on the feedback resistors R1
and R2 to minimize the output voltage spread.
75
Appendix A
Method for Simplifying the
Transfer Function
The expected simplified equation in the numerator or denominator of a transfer function for pole zero calculation is as Equation A.1, where a, b, c are symbolic or numerical terms, where s is Laplace variable.
(1 + as)(1 + bs)(1 + cs) = 0
(A.1)
Assume a, b, c are real, another expression of Equation A.1 is:
abc s3 + (ab + bc + ac) s2 + (a + b + c) s + 1 = 0
p
q
(A.2)
t
Equation A.2 is the form that Matlab transfer function solution are given (with
the calculated symbolic value p, q, t). If the p, q, t are are already known, it is possible
to solve solutions of a, b, c.
Assume abc, we have:
t=a+b+c≈c
(A.3)
Since c is the largest term, which will result the lowest frequency pole or zero (the
dominate one).
Also, p and q have a relation:
q
ab + bc + ac
1 1 1
1
=
= + + ≈
p
abc
a b c
a
(A.4)
which is:
a≈
p
q
(A.5)
a is smallest term, which is actually the highest frequency pole or zero (the least
dominate one).
The intermediate term b can be found as:
76
APPENDIX A. METHOD FOR SIMPLIFYING THE TRANSFER FUNCTION
p = abc
(A.6)
Substituting a and c solutions into Equation A.7, then:
p
q
=
(A.7)
ac
t
Therefore, if the p, q, t of a third order system are given, it is easy to roughly
calculate its separated solutions of a, b, c. It should be noted that this calculation is
only on the assumption that a, b, c are real and widely separated. In cases that a,
b, c are near each other and/or complex numbers, this simplification method will be
inaccurate.
b=
77
Appendix B
The Overall Transfer Function
Calculation
It is true that the total transfer function can be calculated by solving nodal equations.
The small signal behavior of the whole loop is shown in Figure B.1. The nodal
equations can be written as:
V2
GM,OTA
V3
MN
BUF
ROTA
Cgd,MN
COTA1/gm,BUF
Cgs,MN
gm,MN
Vout
C2
R1
V1
R2
C1
Vin
R2
C1
CL
RL
R1
Figure B.1: Signal signal model for the whole loop.
⎧
Vin − V1
V1
⎪
⎪
sC1 (Vin − V1 ) +
=
+ sC2 (V1 − V3 )
⎪
⎪
R
R
1
2
⎪
⎪
⎪
⎪
⎪
⎨ −GM,OT A V1 = V2 + sCOT A V2
ROT A
⎪
⎪
gm,BU F V2 = gm,BU F V3 + sC2 (V3 − V1 ) + sCgd,M N V3 + sCgs,M N (V3 − Vout )
⎪
⎪
⎪
⎪
⎪
Vout
⎪
⎪
⎩ (gm,M N + sCgs,M N )(V3 − Vout ) = sCL Vout +
RL
78
(B.1)
APPENDIX B. THE OVERALL TRANSFER FUNCTION CALCULATION
The transfer function can be calculated by Matlab(see code in Appendix C.4) as1 :
Vout
Vin
1
s4 C1 C2 COT A Cgs,M N R1 R2 RL ROT A + s3 C1 C2 COT A R1 R2 RL ROT A gm,M N
−s2 C1 Cgs,M N GM,OT A R1 R2 RL ROT A gm,BU F
−sC1 GM,OT A R1 R2 RL ROT A gm,M N gm,BU F − GM,OT A R2 RL ROT A gm,M N gm,BU F
≈ 4
s C1 CL COT A (Cgd,M N + Cgs,M N )R1 R2 RL ROT A + s3 C1 CL COT A R1 R2 RL ROT A gm,BU F
+s2 C2 CL GM,OT A R1 R2 RL ROT A gm,BU F + sC2 GM,OT A R1 R2 RL ROT A gm,M N gm,BU F
+gm,BU F (R1 + R2 )(1 + gm,M N RL )
(B.2)
Simplification is based on small numerical terms shown in Appendix C.5
79
Appendix C
Matlab Codes
C.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Gm Calculation
clc ;
clear ;
%%%%%%%%%%%%%%Import data from Cadence s i m u l a t i o n r e s u l t s%%%%%%%%%%%
p l o t D a t a = i m p o r t d a t a ( ’U: \ Simulated Data CSV format \ gm MN plot . c s v ’ ) ;
l o g l o g ( p l o t D a t a . data ( : , 1 ) , p l o t D a t a . data ( : , 2 ) , ’ k ’ , ’ LineWidth ’ , 2 )
x l a b e l ( ’ I { l o a d } (A) ’ , ’ F o n t S i z e ’ , 1 5 ) ;
y l a b e l ( ’Gm(A/V) ’ , ’ F o n t S i z e ’ , 1 5 ) ;
s e t ( gca , ’ F o n t S i z e ’ , 1 5 ) ;%change X,Y Tick f o n t s i z e
h o l d on ;
%%%%%%%%%%%%%%%%%C a l c u l a t e d Model%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%Weak I n v e r s i o n Region ( 2uA−3.5mA)
I o u t =2e −6:1 e − 6 : 3 . 5 e−3
g MN=I o u t / 0 . 0 3 2 5
l o g l o g ( I o u t , g MN , ’−−k ’ , ’ LineWidth ’ , 2 )
h o l d on
%%S a t u r a t i o n Region ( 3 . 5 1mA−120mA)
I o u t =3.51 e −3:1 e −3:120 e−3
g MN=s q r t ( 3 . 4 * I o u t ) ;
l o g l o g ( I o u t , g MN , ’−−k ’ , ’ LineWidth ’ , 2 )
h l e g = l e g e n d ( ’ S i m u l a t e d ’ , ’ C a l c u l a t e d ’ , ’ L o c a t i o n ’ , ’ NorthWest ’ ) ;%l e g e n d c u r v e%
80
APPENDIX C. MATLAB CODES
C.2
Uncompensated Transfer Function Calculation
1 clc ;
2 clear ;
3
4 %For f a s t c a l u c a t i o n s p e e d%
5 %V 1=x , V 2=y , V 3=z%
6
7 syms
s x y z G MOTA R OTA C OTA s g mbuf C gdMN . . .
8
C gsMN g mMN R L C L R 1 R 2 V out V in
9
10 S = s o l v e ( ’−V in *G MOTA* (R OTA/(1+ s *R OTA*C OTA))=x ’ , V in , . . .
11
’ ( x−y ) * g mbuf=s *C gdMN* y+s * C gsMN * ( y−z ) ’ , y , . . .
12
’ ( y−z ) * (g mMN+s * C gsMN)=z / ( R L/(1+ s * R L * C L ) ) ’ , z , . . .
13
’ V out=(R 2 / ( R 1+R 2 ) ) * z ’ , V out ) ;
14
15 TF=(S . V out /S . V in )
16
17 c o l l e c t (TF, s )
C.3
Transfer Function to the gate of MN
1 clc ;
2 clear ;
3
4 %For f a s t c a l u c a t i o n s p e e d%
5 %V 1=x , V 2=y%
6
7 syms
s x y G MOTA R OTA C OTA s g mbuf C gate . . .
8
R 1 R 2 C 1 C 2 V gate V in
9
10 S = s o l v e ( ’ ( V in−x ) / R 1+s * ( V in−x ) * C 1=x/ R 2+s * ( x−V gate ) * C 2 ’ , V in , . . .
11
’−G MOTA* x=y/R OTA+s *C OTA* y ’ , y , . . .
12
’ g mbuf * y=g mbuf * V gate+s * C gate * V gate+s * ( V gate−x ) * C 2 ’ , V gate ) ;
13
14 TF=(S . V gate /S . V in )
15
16 c o l l e c t (TF, s )
C.4
Compensated Transfer Function Calculation
1 clc ;
2 clear ;
3
4 %For f a s t c a l u c a t i o n s p e e d%
5 %V 1=x , V 2=y , V 3=z%
6
7 syms
s x y z G MOTA R OTA C OTA s g mbuf C gdMN . . .
8
C gsMN g mMN R L C L R 1 R 2 C 1 C 2 V out V in
9
10 S = s o l v e ( ’ s * C 1 * ( V in−x)+( V in−x ) / R 1=x/ R 2+s * C 2 * ( x−z ) ’ , V in , . . .
11
’−G MOTA* x=y/R OTA+s *C OTA* y ’ , y , . . .
81
APPENDIX C. MATLAB CODES
12
’ y * g mbuf=g mbuf * z+s * C 2 * ( z−x)+ s *C gdMN* z+s * C gsMN * ( z−V out ) ’ , z , . . .
13
’ (g mMN+s * C gsMN ) * ( z−V out)= s * C L * V out+V out /R L ’ , V out ) ;
14
15 TF=(S . V out /S . V in )
16
17 c o l l e c t (TF, s )
C.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Comparison of Bode Plot
clc ;
clear ;
%Values i n t r a n s f e r f u n c t i o n a p r o x i m a t i o n%%
R 1 =6.26 e6 ;
R 2=2e6 ;
g mbuf=90e −6;
G MOTA=59e −6;
R OTA=1.31 e9 ;
C OTA=0.3 e −12;
C L=220e −9;
C 1=10e −12;
C 2 =1.2 e −12;
C gsMN=14e −12;
C gdMN=8e −12;
R L=1e6 ;%Change t h e l o a d c u r r e n t by R L
I o u t =5/R L
%%%%
%Switch t h e Output Power t r a n s i s t o r between Weak I n v e r s i o n BJT
%and S t a u r a t e d MOS o p e r a t i o n%
i f I o u t <=3.5e−3 %O p e r a t i n g i n BJT mode
g mMN=I o u t / 0 . 0 3 2 5
else
%O p e r a t i n g i n MOSFET mode
g mMN=s q r t ( 3 . 4 * I o u t )
end
%End o f Values i n t r a n f e r f u n c t i o n a p r o x i m a t i o n%
%S i m u l a t i o n r e s u l t s%
subplot (2 ,1 ,1)
%import s i m u l a t e d data%
p l o t D a t a=i m p o r t d a t a ( . . .
’U: \ Simulated Data CSV format \ b o d e p l o t l o w c u r r e n t w i t h m o d i f i e d c k t 0 7 2 6 . c s v ’ ) ;
s e m i l o g x ( p l o t D a t a . data ( : , 1 ) , 2 0 * l o g 1 0 ( abs ( p l o t D a t a . data ( : , 2 ) + 1 j * p l o t D a t a . data ( : , 3 ) ) ) . . .
, ’ k ’ , ’ LineWidth ’ , 1 . 5 )
x l a b e l ( ’ Frequency ( Hz ) ’ , ’ F o n t S i z e ’ , 1 5 ) ;
y l a b e l ( ’ Gain (dB) ’ , ’ F o n t S i z e ’ , 1 5 ) ;
s e t ( gca , ’ F o n t S i z e ’ , 1 5 ) ;%change X,Y Tick f o n t s i z e
h o l d on ;
g r i d on ;
82
APPENDIX C. MATLAB CODES
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
%C a c u l a t i o n r e s u l t%
w = logspace (0 ,10 ,100);
t f =((( C 1 * C 2 *C OTA* C gsMN * R 1 * R 2 * R L *R OTA * ( 1 j *w ) . ˆ 4 ) . . .
+(C 1 * C 2 *C OTA* R 1 * R 2 * R L *R OTA*g mMN) * ( 1 j *w ) . ˆ 3 ) . . .
+((−C 1 * C gsMN *G MOTA* R 1 * R 2 * R L *R OTA* g mbuf ) * ( 1 j *w ) . ˆ 2 ) . . .
+(−C 1 *G MOTA* R 1 * R 2 * R L *R OTA*g mMN* g mbuf * ( 1 j *w ) . ˆ 1 ) . . .
+(−G MOTA* R 2 * R L *R OTA*g mMN* g mbuf ) ) . . .
. / ( ( ( ( C 1 * C L *C OTA*C gdMN* R 1 * R 2 * R L *R OTA . . .
+C 1 * C L *C OTA* C gsMN * R 1 * R 2 * R L *R OTA) * ( 1 j *w ) . ˆ 4 ) . . .
+(( C 1 * C L *C OTA* R 1 * R 2 * R L *R OTA* g mbuf ) * ( 1 j *w ) . ˆ 3 ) . . .
+(C 2 * C L *G MOTA* R 1 * R 2 * R L *R OTA* g mbuf * ( 1 j *w ) . ˆ 2 ) . . .
+(C 2 *G MOTA* R 1 * R 2 * R L *R OTA*g mMN* g mbuf * ( 1 j *w ) . ˆ 1 ) . . .
+(R 1 * g mbuf+R 2 * g mbuf+R 1 * R L *g mMN* g mbuf+R 2 * R L *g mMN* g mbuf ) ) ) ;
f=w/ ( 2 * p i ) ;
s e m i l o g x ( f , 20 * l o g 1 0 ( abs ( t f ) ) , ’−− ’ , ’ LineWidth ’ , 1 . 5 ) ;
h o l d on ;
%Aproximation r e s u l t%
Av=−G MOTA*R OTA * ( R 2 / ( R 1+R 2 ) ) ;
t f 2=Av * ((1+1 j *w* R 1 * C 1 ) . . .
. * (1 −(1 j *w) . ˆ 2 * ( C 2 *C OTA/ (G MOTA* g mbuf ) ) ) . . .
. * (1+1 j *w* C gsMN/g mMN ) ) . . .
. / ( ( 1 + 1 j *w*G MOTA*R OTA* C 2 * ( R 1 * R 2 ) / ( R 1+R 2 ) ) . . .
. * ( 1 + ( 1 j *w) * ( (C OTA* C 1 ) / (G MOTA* C 2 ))+(1 j *w) . ˆ 2 * ( C 1 *C OTA * (C gsMN+C gdMN ) . . .
/ ( g mbuf *G MOTA* C 2 ) ) ) . . .
. * (1+1 j *w* C L/g mMN ) ) ;
s e m i l o g x ( f , 20 * l o g 1 0 ( abs ( t f 2 ) ) , ’ r −. ’ , ’ LineWidth ’ , 1 . 5 ) ;
h o l d on ;
hleg = legend ( ’ Simulated ’ , ’ Calculated ’ , ’ S i m p l i f i e d ’ , . . .
’ L o c a t i o n ’ , ’ NorthEast ’ ) ;
hold o f f ;
%Phase P l o t%
subplot (2 ,1 ,2)
H=180/ p i * a n g l e ( p l o t D a t a . data ( : , 2 ) + 1 j * p l o t D a t a . data ( : , 3 ) ) ;
%1 j f o r complex i n d e x f o r f a s t s p e e d
s e m i l o g x ( p l o t D a t a . data ( : , 1 ) , H, ’ k ’ , ’ LineWidth ’ , 1 . 5 )
h o l d on ;
x l a b e l ( ’ Frequency ( Hz ) ’ , ’ F o n t S i z e ’ , 1 5 ) ;
83
APPENDIX C. MATLAB CODES
99 y l a b e l ( ’ Phase ( Degree ) ’ , ’ F o n t S i z e ’ , 1 5 ) ;
100 s e t ( gca , ’ F o n t S i z e ’ , 1 5 ) ;%change X,Y Tick f o n t s i z e
101
102 %C a c u l a t i o n r e s u l t%
103
104 f=w/ ( 2 * p i ) ;
105 s e m i l o g x ( f , 180/ p i * ( a n g l e ( t f ) ) , ’−− ’ , ’ LineWidth ’ , 1 . 5 ) ;
106 h o l d on ;
107
108 %Approximation r e s u l t%
109
110 s e m i l o g x ( f , 180/ p i * ( a n g l e ( t f 2 ) ) , ’ r −. ’ , ’ LineWidth ’ , 1 . 5 ) ;
111 h o l d o f f ;
112
113 h l e g = l e g e n d ( ’ S i m u l a t e d ’ , ’ C a l c u l a t e d ’ , ’ S i m p l i f i e d ’ , . . .
114
’ L o c a t i o n ’ , ’ NorthEast ’ ) ;
115 g r i d on ;
84
Appendix D
Test-benches
The test-bench used for NMOS linear regulator performance evaluation is shown in
Figure D.1.
NMOS
Linear
Regularor
VOUT
3nH
Line
Transient
Response
Test
25mΩ
220nF
Bond wire model
ESR
Load
Transient
Response
Test
5mΩ
OCP Test
RTEST
GND
Figure D.1: Test-benches.
The RT EST resistance variation in time scale for OCP test is shown in Figure D.2.
RTEST
50Ω
2us
2us
10Ω
10Ω
Time
Figure D.2: RT EST waveform.
85
Appendix E
Current Sink Path
For this linear regulator, the test case of load transient variation from 0μA to 120mA is
not included in Chapter 4, because the power transistor is only able to source current
to the load. The linear regulator can also be treated as a Class A output voltage
buffer. If the load current suddenly reduces to 0A, the power transistor current and
load current difference will charge the output capacitor, making the output voltage
higher than the nominal value.
150
120mA
I (mA)
100
2μs
L
2μs
50
0μA
0
2
0μA
2.5
3
3.5
4
4.5
Time(ms)
5
5.5
6
5
5.5
6
5.2
(V)
4.6
OUT
4.8
V
5
5.022V
W/O Current Sink Path
4.4
4.2
2
2.5
3
3.5
4
4.5
Time(ms)
Figure E.1: Without current sink path.
The power transistor does not have the ability to sink current, the output voltage
reduces only by the discharging path composed by R1 +R2 and CL . Since R1 , R2 , CL
86
APPENDIX E. CURRENT SINK PATH
are all in relative large values. The discharging time constant can be quite long (e.g.
τ ≈1.32s in this design).
In this case, if the output voltage “stucks” at a level higher than its nominal,
the feedback loop will force the gate voltage VG to reduce (in some cases VG may
even below 5V). Then, when the load current suddenly increases, the gate voltage
will experience a larger excursion from low to high than its normal case. For the
larger excursion on VG , the output voltage will have larger spikes which is shown in
Figure E.1. It can be seen that the output voltage is stuck at 5.022V before the IL
increases. This results a large VOU T variation by 700mV.
VBAT
Current
Sink Path
operates
120mA
VREF
VG
MN
IL 0uA
0uA
VOUT
VDDL
R1
C
Isensed
M21
ISINK
M22
R
CL
R2
IL
1:150
M19
M20
M23 M24
M25
GND
Figure E.2: Current sink path circuit.
To solve this problem, a current sink path should be added. The current sink
circuit is active only when the load current varies from high to low. In other cases,
the current sink path should not draw any quiescent current from the linear regulator.
Figure E.2 shows one possible current sink path solution. Again, the output current
is sensed by the circuit described in Section 3.5.1. In normal case, the current from
M22 and M23 are roughly equal, little mismatch current flows into M24 . If M22 and
M23 are chosen to be long channel devices, the channel length modulation effect can
be further reduced, the static mismatch current will be negligible.
When IL changes from 0 to its maximum, the M23 will sink all current from M22 ,
pulling the gate of M25 down to ground, ISIN K ≈0. When IL changes from maximum
to 0, M20 and M23 will shut off. Due to the RC delay, M22 still provides high current.
The current difference between M22 and M23 will sink into M24 which mirrors current
to M25 forming a large amount of current ISIN K .
The effectiveness of this current sink path is simulated and the results are shown in
Figure E.3. It can be seen that during IL from high to low, the peak ISIN K is around
80mA. This ISIN K current peak removes additional charge on CL . The output voltage
can be back to its nominal value after 800μs, the VOU T variation can be reduced to
87
APPENDIX E. CURRENT SINK PATH
70mV, which is nearly 10 times smaller than the case without current sink path.
150
IL(mA)
120mA
100
2μs
2μs
50
0
0
0μA
0μA
0.5
1
1.5
Time(ms)
2
2.5
0.5
1
1.5
Time(ms)
2
2.5
2
2.5
ISink(mA)
100
50
0
0
(V)
4.95
OUT
5
V
5.05
4.9
0
With Current Sinking Path
0.5
1
1.5
Time(ms)
Figure E.3: With current sink path.
88
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